EXHIBIT 4.5(a)


                        LYONDELL PETROCHEMICAL COMPANY

                                      AND

                    CONTINENTAL BANK, NATIONAL ASSOCIATION,

                                                          Trustee
                         FIRST SUPPLEMENTAL INDENTURE

                          Dated as of March 10, 1992

                                    to the

                                   INDENTURE

                          Dated as of March 10, 1992

                             --------------------

                             8.25% Notes Due 1997

                             9.125% Notes Due 2002

 
                               TABLE OF CONTENTS

                                                                         Page
                                                                         ----
            Recitals of the Company.......................................  1
Section 1.  Terms Defined in the Indenture................................  1
Section 2.  Designation...................................................  1
Section 3.  Dating of the Notes...........................................  2
Section 4.  Maximum Aggregate Outstanding Amount..........................  2
Section 5.  Stated Maturity...............................................  2
Section 6.  Denomination of Notes.........................................  2
Section 7.  Payments of Principal and Interest, Record Dates..............  3
Section 8.  Place of Payment..............................................  4
Section 9.  Form of Notes.................................................  4
Section 10. Ranking.......................................................  4
Section 11. Defeasance....................................................  4
Section 12. Definition of Restricted Property and Subsidiary;
            Limitation on Olefins Subsidiary..............................  5
Section 13. Concerning the Trustee........................................  5
Section 14. Governing Law.................................................  6
Section 15. Counterparts..................................................  6
Section 16. Miscellaneous ................................................  6

 
    FIRST SUPPLEMENTAL INDENTURE, dated as of March 10, 1992 (the "Supplement"),
between LYONDELL PETROCHEMICAL COMPANY, a Delaware corporation (the "Company"),
and Continental Bank, National Association, a national banking association (the
"Trustee"), as Trustee under an Indenture, dated as of March 10, 1992 (the
"Indenture").

                            RECITALS OF THE COMPANY

    The Company has previously executed and delivered to the Trustee the
Indenture. Sections 2.01 and 11.01 of the Indenture provide, among other things,
that the Company, when authorized by its Board of Directors, and the Trustee may
at any time and from time to time enter into an indenture supplemental to the
Indenture for the purpose of authorizing a series of Securities and specifying
the terms and form of each series of Securities. The Board of Directors of the
Company has duly authorized the creation, issuance, execution and delivery of
two series of notes consisting of the 8.25% Notes Due 1997 (the "1997 Notes")
and the 9.125% Notes Due 2002 (the "1997 Notes") in the maximum aggregate
principal amount of $200,000,000.

    The Company and the Trustee are executing and delivering this Supplement in
order to provide for the issuance of the 1997 Notes and the 2002 Notes
(collectively the "Notes"). All things necessary to make this Supplement a valid
and legally binding agreement of the Company have been done.

                                   AGREEMENT

    For and in consideration of the premises and the purchase of the Notes by
the Holders thereof, it is mutually covenanted and agreed as follows:

                                  SECTION 1.

                        TERMS DEFINED IN THE INDENTURE.

    All capitalized terms that are used in this Supplement and that are defined
in the Indenture shall have the meanings assigned to them in the Indenture,
except to the extent that such terms are otherwise defined or amended in this
Supplement.

                                  SECTION 2.

                                 DESIGNATION.

    The Notes are hereby created and shall be issuable in two series; the 1997
Notes shall be designated as the "8.25% Notes Due 1997" and the 2002 Notes shall
be designated as the "9.125% Notes Due 2002."

                                       1

 
                                  SECTION 3.

                             DATING OF THE NOTES.

    The Notes shall be dated the date of authentication.

                                  SECTION 4.

                     MAXIMUM AGGREGATE OUTSTANDING AMOUNT.

    The maximum aggregate principal amount of the 1997 Notes and 2002 Notes that
may be authenticated and delivered under this Supplement is limited to
$100,000,000 and $100,000,000, respectively, except for Notes authenticated and
delivered upon transfer of, or in exchange for, or in lieu of, other Notes
pursuant to Sections 2.05, 2.06, 2.07, 3.03 or 11.04 of the Indenture.

                                  SECTION 5.

                               STATED MATURITY.

    The principal amount of the 1997 Notes shall be due and payable on March 15,
1997. The principal amount of the 2002 Notes shall be due and payable on March
15, 2002.

                                  SECTION 6.

                            DENOMINATION OF NOTES.

    The Notes initially will be represented by one or more global securities
(the "Global Securities") deposited with The Depository Trust Company ("DTC")
and registered in the name of a nominee of DTC. Except as set forth below, the
Notes will be available for purchase in denominations of $1,000 and integral
multiples thereof in book-entry form only. The term "Depository" refers to DTC
or any successor depository.

    Upon the issuance by the Company of the Notes represented by the Global
Securities, the Depository or its nominee will credit, on its book-entry
registration and transfer system, the respective principal amounts of the Notes
represented by such Global Securities to the accounts of participants. Ownership
of beneficial interests in the Notes represented by the Global Securities will
be limited to persons who have accounts with DTC ("participants") or persons
that hold interests through participants. Ownership of such beneficial interests
in the Notes will be shown on, and the transfer of that ownership will be
effected only through, records maintained by the Depository (with respect to
interests of participants in the Depository), or by participants in the
Depository or persons that may hold interests through such participants (with
respect to persons other than participants in the Depository).

                                       2

 
    So long as the Depository for a Global Security, or its nominee, is the
registered owner of such Global Security, the Depository or its nominee, as the
case may be, will be considered the sole Holder of the Notes represented by such
Global Security for all purposes under the Indenture. Except as provided below,
owners of beneficial interests in Notes represented by Global Securities will
not be entitled to have the Notes represented by such Global Securities
registered in their names, will not receive or be entitled to receive physical
delivery of the Notes in definitive form and will not be considered the Holders
thereof under the Indenture.

    Payments of principal and interest on the Notes represented by Global
Securities registered in the name of the Depository or its nominee will be made
by the Company through the paying agent to the Depository or its nominee, as the
case may be, as the registered owner of the Notes represented by such Global
Securities.

    If the Depository is at any time unwilling or unable to continue as
Depository and a successor Depository is not appointed by the Company within 90
days, the Company will issue individual Notes in definitive form in exchange for
the Global Securities. In addition, the Company may at any time and in its sole
discretion determine not to have Global Securities, and, in such event, will
issue individual Notes in definitive form in exchange for the Global Securities.
In either instance, the Company will issue Notes in definitive form, equal in
aggregate principal amount to the Global Securities, in such names and in such
principal amounts as the Depository shall request. Notes so issued in definitive
form will be issued in denominations of $1,000 and integral multiples thereof
and will be issued in registered form only, without coupons.

    Neither the Company, the Trustee, any paying agent nor the registrar for the
Notes will have any responsibility or liability for any aspect of the records
relating to or payments made on account of beneficial ownership interests in the
Notes represented by such Global Securities or for maintaining, supervising or
reviewing any records relating to such beneficial ownership interests.

                                  SECTION 7.

               PAYMENTS OF PRINCIPAL AND INTEREST, RECORD DATES.

    Each Note shall bear interest on its outstanding principal balance from
March 19, 1992 at the following interest rates, until payment of the principal
thereof has been made or duly provided for: the 1997 Notes, 8.25%; and the 2002
Notes, 9.125%. Interest on the Notes shall be paid semi-annually on March 15 and
September 15, commencing on September 15, 1992. Interest on the Notes of each
series shall be computed on the basis of a 360-day year of twelve 30-day months,
from the later of: (1) March 19, 1992, or (2) the most recent Interest Payment
Date next preceding the date of such Note to which interest has been paid or
duly provided for (unless the date of such Note is an Interest Payment Date, in
which case the date of such Note). Interest on the Notes shall be payable in
lawful money of the United States of America.

    The principal of each Note shall be payable on the date due upon delivery
and surrender of such Note to the Trustee at the Place of Payment in lawful
money of the United States of America in next-day funds by check as provided in
Section 5.02 of the Indenture.

    The record date ("Record Date") for each Interest Payment Date shall be the
close of business on the March 1 and September 1 next preceding each Interest
Payment Date, whether or not such date shall be a Business Day.

    Any interest not paid on the Interest Payment Date therefor ("Defaulted
Interest") may be paid to the person in whose name the Note is registered at the
close of business on a special record date for the payment of such Defaulted
Interest, notice of which shall be given by the Company to Holders of Notes not
less than fifteen days prior to such special record date, or may be paid in any
other lawful manner.

                                       3

 
    At the option of the Company, payment of interest on each Note shall be made
on each Interest Payment Date to the Holder of each Note at the close of
business on the Record Date for each Interest Payment Date by check mailed to
the Holder at its address as it appears on the registration books maintained by
the Company pursuant to Section 2.05 of the Indenture or at any other address
that is furnished to the Trustee in writing by the Holder at least 15 Business
Days prior to the Interest Payment Date.

    Any payment of principal or interest required to be made on an Interest
Payment Date or at Maturity of a Note that is not a Business Day need not be
made on that day, but may be made on the next succeeding Business Day with the
same force and effect as if made on the Interest Payment Date or at Maturity, as
the case may be, and no additional interest shall accrue as a result of such
delayed payment. The Company shall pay any administrative costs imposed by banks
in connection with any election by the Company, in its sole discretion, to make
payments by wire transfer in accordance with the requirements of this Section 7,
but any tax, assessment or governmental charge imposed upon or required to be
withheld from payments shall be borne by the Holders of the Notes in respect to
which payments are made.

                                   SECTION 8.

                               PLACE OF PAYMENT.

    The Place of Payment of the Notes shall be at the offices or agencies of the
Trustee in Chicago, Illinois or the Borough of Manhattan, the City of New York,
New York, which shall be maintained for such purpose in accordance with Section
5.02 of the Indenture.

                                  SECTION 9.

                                FORM OF NOTES.

    The form of the 1997 Notes and the 2002 Notes are attached hereto as
Exhibits A-I and A-II, respectively. Each of the 1997 Notes shall be numbered
consecutively from A-1 upward. Each of the 2002 Notes shall be numbered
consecutively from B-1 upward. The Notes shall bear CUSIP numbers, but any
failure to indicate or any error in such CUSIP numbers shall not in any way
affect the validity of the Notes.

                                  SECTION 10.

                                   RANKING.

    The Notes shall constitute unsecured and unsubordinated indebtedness of the
Company and shall rank pari passu with any other unsecured and unsubordinated
indebtedness of the Company.


                                       4

 
                                  SECTION 11.

                                  DEFEASANCE.

    The Notes shall be subject to defeasance as provided in Article Fourteen of
the Indenture. Upon any defeasance of the 1997 Notes or 2002 Notes, the Company
shall cease to be under any obligation to comply with any term, provision or
condition of Section 12 of this Supplement.

                                  SECTION 12.

               DEFINITION OF RESTRICTED PROPERTY AND SUBSIDIARY;

                    LIMITATION ON OLEFINS SUBSIDIARY DEBT.

    The definition of Restricted Property in the Indenture shall be amended (i)
to include any plant for the refining of petroleum or the production of
petrochemicals that as of the date hereof is leased by the Company or its
Subsidiary. The definition of Restricted Subsidiary in the Indenture shall be
amended to include any Subsidiary that as of the date hereof leases Restricted
Property.

    During any period that title to the Company's two olefins plants located at
Channelview, Texas ("Olefins Plants") is owned by one or more Subsidiaries (for
purposes of this Section 12 hereinafter referred to collectively as the "Olefins
Subsidiary"), the Company shall not permit any Olefins Subsidiary to issue,
guarantee, assume, incur or have outstanding directly or indirectly, any Debt
(as defined in Section 5.03 of the Indenture); provided, however, that this
limitation shall not apply to Debt secured by Mortgages permissible under
clauses (a) through (h) of Section 5.03 of the Indenture; and, further provided,
that the term Olefins Plants shall not include (i) the Company's methanol plant
and other petrochemical processing units located on the same site as the Olefins
Plants, or (ii) the polypropylene plant or the low density polyethylene plant
located in Pasadena, Texas that as of the date hereof is owned by a Subsidiary
of the Company. Notwithstanding the foregoing, an Olefins Subsidiary may issue,
assume, guarantee or have outstanding Debt which would otherwise be subject to
the foregoing restriction in an aggregate principal amount which, together with
the outstanding principal amount of (A) any Debt permitted under the last
paragraph of Section 5.03 of the Indenture and (B) all other Debt of an Olefins
Subsidiary subject to the foregoing restriction, does not at any one time exceed
the greater of $50 million or 10% of the Consolidated Net Tangible Assets of the
Company and its consolidated Subsidiaries.

    Except as provided above, the definitions contained in, and Section 5.03 of,
the Indenture shall remain unchanged. The amendments and provisions set forth in
this Section 12 shall not affect any Security of any series created after the
date of this Supplement.

                                  SECTION 13.

                            CONCERNING THE TRUSTEE.

    (A) Subject to the provisions of the Trust Indenture Act of 1939, Section
8.02 of the Indenture shall be amended to add the following clause as Clause 
(i):

                                       5

 
    "(i) the Trustee shall not be required to take notice of or be deemed to
    have notice of any Event of Default under the Indenture, except for Events
    of Default specified in Subsection (a), (b) or (c) of Section 7.01 of the
    Indenture, unless the Trustee shall be specifically notified in writing of
    such Event of Default by the Company or any Holder of the Notes, and all
    notices in order to be effective must be delivered to the Principal Office
    of the Trustee, and in the absence of such notice so delivered, the Trustee
    may conclusively assume there is no Event of Default except as
    aforementioned."

    (B) Subject to the provisions of the Trust Indenture Act of 1939, Section
9.04 of the Indenture shall be amended to add at the end of Section 9.04 the
following paragraph:

    "Upon request of the Trustee, the Company shall furnish the Trustee promptly
    an Officer's Certificate listing and identifying all Notes if any, known by
    the Company to be owned or held by or for the account of any of the above
    described persons; and subject to Sec. 8.01, the Trustee shall be authorized
    to accept such Officer's Certificate as conclusive evidence of the facts
    therein set forth and the fact that all Notes not listed therein are
    outstanding for the purpose of any such determination."

    (C) Except as provided above, Sections 8.02 and 9.04 of the Indenture shall
remain unchanged. The amendments and provisions set forth in this Section 13
shall not affect any Security of any series created after the date of this
Supplement.

                                  SECTION 14.

                                GOVERNING LAW.

    THIS SUPPLEMENT AND EACH NOTE ISSUED HEREUNDER SHALL BE CONSTRUED IN
ACCORDANCE WITH AND GOVERNED BY THE LAWS OF THE STATE OF NEW YORK APPLICABLE TO
AGREEMENTS MADE AND TO BE PERFORMED THEREIN.

                                  SECTION 15.

                                 COUNTERPARTS.

    This Supplement may be executed in any number of counterparts, each of which
so executed shall be deemed to be an original, but both of which shall together
constitute but one and the same instrument.

                                  SECTION 16.

                                MISCELLANEOUS.

    (a) Except as expressly amended and supplemented by this Supplement, the
Indenture shall remain unchanged and in full force and effect.

                                       6

 
    (b) This Supplement shall be construed as supplemental to the Indenture and
shall form a part thereof. 

    IN WITNESS WHEREOF, the Company and the Trustee have caused this Supplement
to be duly executed by their respective officers thereunto duly authorized as of
the day and year first above written.

                                          LYONDELL PETROCHEMICAL COMPANY


                                          By:  /s/ Russell S. Young            
                                               ------------------------------- 
                                          Name:        Russell S. Young        
                                          Title:  Vice President and Treasurer 

 



                                          CONTINENTAL BANK, NATIONAL
                                          ASSOCIATION, as Trustee


                                          By:  /s/ Greg Jordan                
                                               -------------------------------
                                          Name:        Greg Jordan            
                                          Title:      Vice President 


                                       7

 
                                 EXHIBIT A-I 
 
    Unless this certificate is presented by an authorized representative of The
Depository Trust Company, a New York corporation ("DTC"), to the Issuer or its
agent for registration of transfer, exchange, or payment, and any certificate
issued is registered in the name of Cede & Co. or in such other name as
requested by an authorized representative of DTC (and any payment is made to
Cede & Co. or such other entity as is requested by an authorized representative
of DTC), ANY TRANSFER, PLEDGE, OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR
TO ANY PERSON IS WRONGFUL inasmuch as the registered owner hereof, Cede & Co.,
has an interest herein.

                        LYONDELL PETROCHEMICAL COMPANY

                             8.25% NOTE DUE 1997               CUSIP 552078 AC 1

No. A-1                                                        $100,000,000

    LYONDELL PETROCHEMICAL COMPANY, a corporation duly organized and existing
under the laws of the State of Delaware (herein called the "Company"), for value
received, hereby promises to pay to Cede & Co., or registered assigns, the
principal sum of $100,000,000 at the office or agency of the Trustee (herein
defined) in The City of Chicago, Illinois or in the Borough of Manhattan, The
City of New York, on March 15, 1997, in such coin or currency of the United
States of America as at the time of payment shall be legal tender for payment of
public and private debts, and to pay interest thereon from March 19, 1992, or
from the most recent March 15 or September 15 next preceding the date of this
Note to which interest has been paid or duly provided for (unless the date
hereof is the date to which interest on the Notes has been paid, in which case
from the date of this Note), semiannually on March 15 and September 15 of each
year (each an "Interest Payment Date"), commencing September 15, 1992, on said
principal sum at said office or agency, in like coin or currency, at the rate
per annum specified in the title hereof, until the principal hereof is paid or
duly provided for. The interest so payable on any Interest Payment Date will be
paid, except as provided in the Indenture (herein defined), to the person in
whose name this Note is registered at the close of business on the Record Date
for such interest, which shall be the March 1 or September 1 (whether or not a
Business Day), as the case may be, next preceding such Interest Payment Date;
provided, however, that at the option of the Company payment of interest may be
made by check mailed to the address of such person as such address shall appear
in the register for the Notes. For purposes of this Note, "Business Day" means
any day, other than a Saturday or Sunday, that is not a day on which banking
institutions are authorized or required by law or regulation to be closed in The
City of Chicago or The City of New York or The City of Houston.

    Interest will be computed on the basis of a 360-day year of twelve 30-day
months.

    This Note shall not be valid or become obligatory for any purpose until the
certificate of authentication hereon shall have been signed by the Trustee under
the Indenture.

    This Note is one of a duly authorized issue of debentures, notes or other
evidences of indebtedness of the Company (herein called the "Securities"), of
the series hereinafter specified, all issued or to be issued under and pursuant
to an Indenture dated as of March 10, 1992 (herein called the "Indenture"), duly
executed and delivered by the Company to Continental Bank, National Association,
as trustee (hereinafter called the "Trustee"), to which Indenture, and all
indentures supplemental thereto, reference is hereby made for a description of
the rights, limitation of rights, obligations, duties and immunities thereunder
of the Trustee, the Company and the Holders of the Securities. The Securities
may be issued in one or more series, which different series may be issued in
various aggregate principal amounts, may mature at different times, may bear
interest (if any) at different rates, may be subject to different redemption
provisions (if any), may be subject to different sinking, purchase or analogous
funds (if any), may be subject to different covenants and Events of Default and
may otherwise vary as provided in the Indenture. In the event of any
inconsistency between the provisions of this Note and the provisions of the
Indenture, and any indentures supplemental thereto, the terms of the Indenture
and any indentures supplemental thereto shall control. Each Holder of this Note
by accepting the


                                       1

 
same, agrees to and shall be bound by the provisions of the Indenture.

    This Note is one of a series of Securities of the Company issued pursuant to
the First Supplemental Indenture dated as of March 10, 1992 (herein called the
"Supplement"), and the Indenture (as used herein the "Indenture" refers to the
Indenture as supplemented by the Supplement) designated as the 8.25% Notes Due
1997 (herein called the "Notes") limited in aggregate principal amount to
$100,000,000.

    In case an Event of Default with respect to the Notes shall occur and be
continuing, the principal hereof may be declared, and upon such declaration
shall become, due and payable, in the manner, with the effect and subject to the
conditions provided in the Indenture.

    The Indenture contains provisions permitting the Company and the Trustee,
with the consent of the Holders of not less than 50% in aggregate principal
amount at Stated Maturity of the Securities at the time outstanding of each
series affected by such supplemental indenture or indentures, evidenced as
provided in the Indenture, to execute supplemental indentures adding any
provisions to or changing in any manner or eliminating any of the provisions of
the Indenture, or of any supplemental indenture or indentures, as such
provisions apply to such Securities, or modifying in any manner the rights of
the Holders of the Securities of each such series; provided, however, that no
such supplemental indenture shall, without the consent of the Holders of each
Security of such series so affected, thereby, (i) extend the fixed maturity of
any Security or reduce the rate or extend the time of payment of interest
thereon or reduce the principal thereof or the time during which premium is
payable thereon or change the method of computing the amount of principal
thereof or make the principal thereof or any premium or interest thereon payable
in any coin or currency other than that provided in the Securities, or (ii)
reduce the percentage in principal amount at Stated Maturity of the outstanding
Securities, the consent of the Holders of which is required for any such
supplemental indenture, or the consent of the Holders of which is required for
any waiver of compliance with certain provisions of the Indenture or of certain
defaults under, and their consequences provided for in, the Indenture. Any such
consent or waiver by the Holder of this Note (unless revoked as provided in the
Indenture) shall be conclusive and binding upon such Holder and upon all future
Holders and owners of this Note and any Notes which may be issued in exchange or
substitution herefor, irrespective of whether any notation thereof is made upon
this Note or such other Notes.

    No reference herein to the Indenture and no provision of this Note or of
the Indenture shall alter or impair the obligation of the Company, which is
absolute and unconditional, to pay the principal of and interest on this Note at
the place, at the respective times, at the rate, and in the coin or currency
herein prescribed.

    The Notes may not be redeemed prior to maturity. The Notes are unsecured
obligations of the Company ranking pari passu without any preference among
themselves and equally with all other unsecured indebtedness (other than
subordinated indebtedness) of the Company from time to time outstanding.

    The Notes are issuable in registered form without coupons in denominations
of $1,000 and whole multiples of $1,000 in excess of that amount. Notes may be
exchanged for a like aggregate principal amount of Notes of other authorized
denominations, without charge except for any tax or other governmental charge
imposed in relation thereto, at the office or agency of the Trustee in The City
of Chicago and in the Borough of Manhattan, The City of New York, and in the
manner and subject to the limitations provided in the Indenture.

    Upon due presentment for registration of transfer of this Note at the office
or agency of the Trustee in The City of Chicago or the Borough of Manhattan, The
City of New York, a new Note or Notes of authorized denominations for an equal
aggregate principal amount at Stated Maturity will be issued to the transferee
in exchange therefor, in the manner and subject to the limitations provided in
the Indenture, without charge except for any tax or other governmental charge
imposed in relation thereto.

    Prior to due presentment for registration of transfer of this Note, the
Company, the Trustee, any paying agent and any registrar for the Notes may deem
and treat the registered Holder hereof as the absolute owner of this Note
(whether or not this Note shall be overdue and notwithstanding any notation of
Ownership or other writing hereon by anyone other than the Company, any
registrar for the Notes or the Trustee), for the purpose of receiving payment
hereof or on account hereof, and for all other purposes (subject to the
provisions of the first paragraph hereof), and neither the Company nor the
Trustee nor any paying agent nor any registrar for the Notes shall be affected
by any notice to the contrary.

                                       2

 
    No recourse for the payment of the principal of or premium, if any, or
interest on this Note, or for any claim based hereon or otherwise in respect
hereof, and no recourse under or upon any obligation, covenant or agreement of
the Company in the Indenture, or any indenture supplemental thereto, or in any
Note, or because of the creation of any indebtedness represented thereby, shall
be had against any incorporator, stockholder, officer or director, as such,
past, present or future, of the Company or of any successor corporation, either
directly or through the Company or any successor corporation, whether by virtue
of any constitution, statute or rule of law or by the enforcement of any
assessment or penalty or otherwise, all such liability being, by the acceptance
hereof and as a condition of and as part of the consideration for the issue
hereof, expressly waived and released.

    Terms used herein which are defined in the Indenture shall have the meanings
assigned to them in the Indenture.

    THIS NOTE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAW OF
THE STATE OF NEW YORK.

    IN WITNESS WHEREOF, LYONDELL PETROCHEMICAL COMPANY has caused this
instrument to be signed, manually or by facsimile, by its duly authorized
officers, and its corporate seal to be printed, engraved or otherwise reproduced
hereon, by facsimile or otherwise.

                        LYONDELL PETROCHEMICAL COMPANY


By                                        By

- --------------------------------          -------------------------------------
Vice President and Treasurer              President and Chief Executive Officer

Dated: March 19, 1992

                    TRUSTEE'S CERTIFICATE OF AUTHENTICATION

    THIS IS ONE OF THE SECURITIES ISSUED UNDER THE WITHIN-MENTIONED INDENTURE.

                CONTINENTAL BANK, NATIONAL ASSOCIATION, AS TRUSTEE



                      BY _________________________________
                                Authorized Officer

Dated: March 19, 1992


                                       3

 
                                 EXHIBIT A-II

    Unless this certificate is presented by an authorized representative of The
Depository Trust Company, a New York corporation ("DTC"), to the Issuer or its
agent for registration of transfer, exchange, or payment, and any certificate
issued is registered in the name of Cede & Co. or in such other name as
requested by an authorized representative of DTC (and any payment is made to
Cede & Co. or such other entity as is requested by an authorized representative
of DTC), ANY TRANSFER, PLEDGE, OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR
TO ANY PERSON IS WRONGFUL inasmuch as the registered owner hereof, Cede & Co.,
has an interest herein.

                        LYONDELL PETROCHEMICAL COMPANY

                             9.125% NOTE DUE 2002              CUSIP 552078 AD 9

No. B-1                                                        $100,000,000

    LYONDELL PETROCHEMICAL COMPANY, a corporation duly organized and existing
under the laws of the State of Delaware (herein called the "Company"), for value
received, hereby promises to pay to Cede & Co., or registered assigns, the
principal sum of $100,000,000 at the office or agency of the Trustee (herein
defined) in The City of Chicago, Illinois or in the Borough of Manhattan, The
City of New York, on March 15, 2002, in such coin or currency of the United
States of America as at the time of payment shall be legal tender for payment of
public and private debts, and to pay interest thereon from March 19, 1992, or 
from the most recent March 15 or September 15 next preceding the date of this
Note to which interest has been paid or duly provided for (unless the date
hereof is the date to which interest on the Notes has been paid, in which case
from the date of this Note), semiannually on March 15 and September 15 of each
year (each an "Interest Payment Date"), commencing September 15, 1992, on said
principal sum at said office or agency, in like coin or currency, at the rate
per annum specified in the title hereof, until the principal hereof is paid or
duly provided for. The interest so payable on any Interest Payment Date will be
paid, except as provided in the Indenture (herein defined), to the person in
whose name this Note is registered at the close of business on the Record Date
for such interest, which shall be the March 1 or September 1 (whether or not a
Business Day), as the case may be, next preceding such Interest Payment Date;
provided, however, that at the option of the Company payment of interest may be
made by check mailed to the address of such person as such address shall appear
in the register for the Notes. For purposes of this Note, "Business Day" means
any day, other than a Saturday or Sunday, that is not a day on which banking
institutions are authorized or required by law or regulation to be closed in The
City of Chicago or The City of New York or The City of Houston.

    Interest will be computed on the basis of a 360-day year of twelve 30-day
months.
 
    This Note shall not be valid or become obligatory for any purpose until the
certificate of authentication hereon shall have been signed by the Trustee under
the Indenture.

    This Note is one of a duly authorized issue of debentures, notes or other
evidences of indebtedness of the Company (herein called the "Securities"), of 
the series hereinafter specified, all issued or to be issued under and pursuant
to an Indenture dated as of March 10, 1992 (herein called the "Indenture"), duly
executed and delivered by the Company to Continental Bank, National Association,
as trustee (hereinafter called the "Trustee"), to which Indenture, and all
indentures supplemental thereto, reference is hereby made for a description of
the rights, limitation of rights, obligations, duties and immunities thereunder
of the Trustee, the Company and the Holders of the Securities. The Securities
may be issued in one or more series, which different series may be issued in
various aggregate principal amounts, may mature at different times, may bear
interest (if any) at different rates, may be subject to different redemption
provisions (if any), may be subject to different sinking, purchase or analogous
funds (if any), may be subject to different covenants and Events of Default and
may otherwise vary as provided in the Indenture. In the event of any
inconsistency between the provisions of this Note and the provisions of the
Indenture, and any indentures supplemental thereto, the terms of the

                                       1

 
Indenture and any indentures supplemental thereto shall control. Each Holder of
this Note by accepting the same, agrees to and shall be bound by the provisions
of the Indenture.

    This Note is one of a series of Securities of the Company issued pursuant to
the First Supplemental Indenture dated as of March 10, 1992 (herein called the
"Supplement"), and the Indenture (as used herein the "Indenture" refers to the
Indenture as supplemented by the Supplement) designated as the 9.125% Notes Due
2002 (herein called the "Notes") limited in aggregate principal amount to
$100,000,000.

    In case an Event of Default with respect to the Notes shall occur and be
continuing, the principal hereof may be declared, and upon such declaration
shall become, due and payable, in the manner, with the effect and subject to
the conditions provided in the Indenture.

    The Indenture contains provisions permitting the Company and the Trustee,
with the consent of the Holders of not less than 50% in aggregate principal
amount at Stated Maturity of the Securities at the time outstanding of each
series affected by such supplemental indenture or indentures, evidenced as
provided in the Indenture, to execute supplemental indentures adding any
provisions to or changing in any manner or eliminating any of the provisions of
the Indenture, or of any supplemental indenture or indentures, as such
provisions apply to such Securities, or modifying in any manner the rights of
the Holders of the Securities of each such series; provided, however, that no
such supplemental indenture shall, without the consent of the Holders of each
Security of such series so affected, thereby, (i) extend the fixed maturity of
any Security or reduce the rate or extend the time of payment of interest
thereon or reduce the principal thereof or the time during which premium is
payable thereon or change the method of computing the amount of principal
thereof or make the principal thereof or any premium or interest thereon payable
in any coin or currency other than that provided in the Securities, or (ii)
reduce the percentage in principal amount at Stated Maturity of the outstanding
Securities, the consent of the Holders of which is required for any such
supplemental indenture, or the consent of the Holders of which is required for
any waiver of compliance with certain provisions of the Indenture or of certain
defaults under, and their consequences provided for in, the Indenture. Any such
consent or waiver by the Holder of this Note (unless revoked as provided in the
Indenture) shall be conclusive and binding upon such Holder and upon all future
Holders and owners of this Note and any Notes which may be issued in exchange or
substitution herefor, irrespective of whether any notation thereof is made upon
this Note or such other Notes.

    No reference herein to the Indenture and no provision of this Note or of the
Indenture shall alter or impair the obligation of the Company, which is absolute
and unconditional, to pay the principal of and interest on this Note at the
place, at the respective times, at the rate, and in the coin or currency herein
prescribed.

    The Notes may not be redeemed prior to maturity. The Notes are unsecured
obligations of the Company ranking pari passu without any preference among
themselves and equally with all other unsecured indebtedness (other than
subordinated indebtedness) of the Company from time to time outstanding.

    The Notes are issuable in registered form without coupons in denominations
of $1,000 and whole multiples of $1,000 in excess of that amount. Notes may be
exchanged for a like aggregate principal amount of Notes of other authorized
denominations, without charge except for any tax or other governmental charge
imposed in relation thereto, at the office or agency of the Trustee in The City
of Chicago and in the Borough of Manhattan, The City of New York, and in the
manner and subject to the limitations provided in the Indenture.

    Upon due presentment for registration of transfer of this Note at the office
or agency of the Trustee in The City of Chicago or the Borough of Manhattan,
The City of New York, a new Note or Notes of authorized denominations for an
equal aggregate principal amount at Stated Maturity will be issued to the
transferee in exchange therefor, in the manner and subject to the limitations
provided in the Indenture, without charge except for any tax or other
governmental charge imposed in relation thereto.

    Prior to due presentment for registration of transfer of this Note, the
Company, the Trustee, any paying agent and any registrar for the Notes may deem
and treat the registered Holder hereof as the absolute owner of this Note
(whether or not this Note shall be overdue and notwithstanding any notation of
ownership or other writing hereon by anyone other than the Company, any
registrar for the Notes or the Trustee), for the purpose of receiving payment
hereof or on account hereof, and for all other purposes (subject to the
provisions of the first paragraph hereof), and neither the Company nor the 
Trustee nor any paying agent nor any registrar for the

                                       2

 
Notes shall be affected by any notice to the contrary.

    No recourse for the payment of the principal of or premium, if any, or
interest on this Note, or for any claim based hereon or otherwise in respect
hereof, and no recourse under or upon any obligation, covenant or agreement of
the Company in the Indenture, or any indenture supplemental thereto, or in any
Note, or because of the creation of any indebtedness represented thereby, shall
be had against any incorporator, stockholder, officer or director, as such,
past, present or future, of the Company or of any successor corporation, either
directly or through the Company or any successor corporation, whether by virtue
of any constitution, statute or rule of law or by the enforcement of any
assessment or penalty or otherwise, all such liability being, by the acceptance
hereof and as a condition of and as part of the consideration for the issue
hereof, expressly waived and released.

    Terms used herein which are defined in the Indenture shall have the meanings
assigned to them in the Indenture.

    THIS NOTE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAW OF
THE STATE OF NEW YORK.

    IN WITNESS WHEREOF, LYONDELL PETROCHEMICAL COMPANY has caused this
instrument to be signed, manually or by facsimile, by its duly authorized
officers, and its corporate seal to be printed, engraved or otherwise reproduced
hereon, by facsimile or otherwise.

                        LYONDELL PETROCHEMICAL COMPANY

By                                         By

- ---------------------------------          -----------------------------------
  Vice President and Treasurer             President and Chief Executive Officer

Dated: March 19, 1992

                    TRUSTEE'S CERTIFICATE OF AUTHENTICATION

    THIS IS ONE OF THE SECURITIES ISSUED UNDER THE WITHIN-MENTIONED INDENTURE.


              CONTINENTAL BANK, NATIONAL ASSOCIATION, AS TRUSTEE



                   By  ___________________________________
                              Authorized Officer

Dated: March 19, 1992


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