RESOLUTIONS OF THE
                              BOARD OF DIRECTORS OF
                               HALLIBURTON COMPANY
                          EFFECTIVE SEPTEMBER 28, 1998


                  WHEREAS,  the Board of Directors of the Company has heretofore
         authorized  the offering  from time to time,  at an  aggregate  initial
         offering price of up to  $500,000,000,  of  Medium-Term  Notes Due Nine
         Months or More From Date of Issue, Series A (the "Series A Notes"), and
         the Company  has  registered  the  offering,  sale and  delivery of the
         Series A Notes  pursuant  to the  Securities  Act of 1933,  as amended,
         pursuant  to  a   Registration   Statement  on  Form  S-3  (the  "First
         Registration   Statement")  filed  with  the  Securities  and  Exchange
         Commission (the "Commission"); and

                  WHEREAS, to date Series A Notes,  offered by the Company at an
         aggregate initial offering price of $300,000,000,  have been issued and
         sold by the Company under the First Registration Statement; and

                  WHEREAS,  the Board of Directors of the Company has determined
         that the  requirements  of the Company  for long term debt  capital may
         exceed  $200,000,000,  the amount of Series A Notes remaining available
         for sale and that, therefore, it is in the best interest of the Company
         to establish an additional Medium Term Notes Program; and

                  WHEREAS,  pursuant to resolutions  theretofore  adopted by the
         Board of  Directors of the Company,  the Company  filed a  Registration
         Statement on Form S-3 (the "Second  Registration  Statement") on August
         1, 1997  relating to the  offering  from time to time,  at an aggregate
         initial   offering  price  of  up  to   $600,000,000,   of  senior  and
         subordinated debt securities of the Company, none of which has yet been
         offered or sold; and

                  WHEREAS,  subject  to  certain  limitations,   this  Board  of
         Directors  deems it  appropriate  to delegate its  authority to certain
         officers  of the  Company  in  connection  with the  Series B Notes (as
         hereinafter  defined)  that are not  originally  offered  at one  time,
         including the authority to fix the terms of such Series B Notes; and

                  WHEREAS,  terms  used in the  following  resolutions  (and not
         otherwise  defined  therein) are defined in the Second Senior Indenture
         dated as of December  1,1996,  among the predecessor of the Company and
         Texas Commerce Bank National  Association  (now Chase Bank of Texas, N.
         A. and herein called the "Trustee") as the same has heretofore been and
         may  hereafter  be  amended  or   supplemented   (the  "Second   Senior
         Indenture");




         NOW, THEREFORE, BE IT:

                  RESOLVED,  that this Board of Directors does hereby  authorize
         the  issuance  under  the  Second  Senior  Indenture  of  a  series  of
         securities  with terms, in addition to the terms provided in the Second
         Senior  Indenture  with  respect  to  Securities  of  a  series  issued
         thereunder, as follows:

                  (i)    The  title of  the Securities is "Medium-Term Notes Due
         Nine  Months or  More  From  Date  of  Issue,  Series B" (the "Series B
         Notes").

                  (ii)   The Series B Notes are limited in  aggregate  principal
         amount to the amount that may be sold at an aggregate initial  offering
         price of up to  $600,000,000,  subject  to  reduction  by the aggregate
         initial  offering price of Securities other than the Series A Notes and
         the Series B Notes sold pursuant to the Second  Senior Indenture or the
         Subordinated   Indenture   (as   defined  in  the  Second  Registration
         Statement). Subject to the foregoing, the aggregate principal amount of
         the Series B Notes to be issued  and sold from time to time shall be as
         (i) determined on behalf of the Company by the Chief Executive Officer,
         the  President  and   Chief  Operating  Officer,   any  Executive  Vice
         President, the Vice President and  Treasurer or the Vice  President and
         Secretary  (each  an  "Authorized  Officer")  and  (ii)  set forth in a
         written  request to the Trustee for authentication (an  "Authentication
         Request") signed by  an Authorized  Officer or  any Vice President, any
         Assistant Treasurer, the Controller, or any other officer  or  employee
         of the Company designated  in writing  by any two  Authorized  Officers
         (each  of the foregoing, a "Designated Person").

                  (iii)  The Series B Notes may be issued only as Senior  Notes.
         The Series B Notes  will  rank  equally  with all other  unsecured  and
         unsubordinated indebtedness of the Company. The Series B Notes may also
         be issued as original issue  discount  notes  ("OID  Notes") and may be
         issued as Global Securities. They may also be issued with the amount of
         principal (and premium, if any) and/or any interest  payable in respect
         thereof  to be  determined  with  reference  to the price or  prices of
         specified  commodities  or  stocks  or  other price  or  exchange  rate
         ("Indexed Notes").

                  (iv)   Any  interest on the  Series  B Notes  will be  payable
         generally to the person in whose name a Note is registered at the close
         of business  on the Regular  Record  Date next  preceding the  Interest
         Payment Date; provided, however, that interest payable at maturity will
         be payable to the person to whom principal shall be payable.

                  (v)    The date on which the principal of each of the Series B
         Notes is payable shall be any day nine months or later from its date of
         issue,  as determined  on behalf of the Company from time to time by an
         Authorized Officer and set forth in an Authentication Request.




                  (vi)   Each Note, other  than an OID Note,  will bear interest
         at  either: a  fixed  rate  (a "Fixed Rate  Note") or  a variable  rate
         determined by  reference to an interest  rate formula (a "Floating Rate
         Note").

                  (vii)  Unless otherwise  indicated in the Pricing  Supplement,
         the Regular Record Date for any Floating Rate Note shall be the date 15
         calendar  days before each  Interest Payment  Date whether  or not such
         date shall be a Business  Day and the  Interest  Payment  Dates for any
         Fixed Rate Note shall be March 31 and September 30 of each year.

                  (viii) Unless otherwise determined on behalf of the Company by
         an  Authorized  Officer  and set  forth  in an  Authentication Request,
         payments of principal of, premium, if any, and interest on the Series B
         Notes shall be at the corporate trust office maintained by the Trustee,
         as paying  agent, in The  City of  New  York, or such  other  office or
         agency as may be designated by the Company; provided, however,  that at
         the option of the Company payment of interest (other than  interest  at
         maturity)  may be made by check  mailed  to the  address of the  Person
         entitled  thereto  at such  address  as  shall appear  in the  Security
         Register;  and  provided,  further,  that payment of the  principal of,
         premium, if any,  and interest  due on any  Note which  is a Book-Entry
         Note  will be  made in  immediately available  funds at  such corporate
         trust office or such other office or agency.

                  (ix)   If so specified  in the applicable  Pricing Supplement,
         the Series  B Notes  will be  repayable by the Company in whole or from
         time to  time in  part  at the  option  of the  Holders  thereof on the
         optional repayment dates ("Optional Repayment Dates") specified in such
         Pricing Supplement.

                  (x)    The right, if any, of the Company to redeem each of the
         Series B Notes,  in whole or in part, at its  option  and the period or
         periods  within  which, the  price or prices at which and the terms and
         conditions  upon  which such  Note  may  be  so  redeemed  shall  be as
         established on behalf of the Company by an  Authorized  Officer and set
         forth in the applicable Pricing Supplement.

                  (xi)  The Series B Notes may be denominated in U.S. dollars or
         in  such  other  currency  or  composite currency  unit  (a  "Specified
         Currency")  as  indicated in the  applicable  Pricing  Supplement, and,
         unless  otherwise   specified  in  the  applicable Pricing  Supplement,
         payments of principal of, premium, if any, and interest on the Series B
         Notes  may  be  made  only  in  U.S. dollars.  If so  specified  in the
         applicable  Pricing  Supplement, payments of principal of, premium,  if
         any, and interest on the Series B Notes denominated  in other than U.S.
         dollars  will be made in the  Specified  Currency at the  option of the
         Holders thereof.

                  (xii)  Unless otherwise determined on behalf of the Company by
         an Authorized Officer and set forth in an Authentication  Request,  the
         Series B Notes (other than Global Notes representing  Book-Entry Notes)
         denominated in U.S. dollars ("U.S. Currency Notes") will be issued only
         in  fully  registered  form  in  minimum  denominations  of $1,000 and
         integral multiples thereof.  Notes denominated in a  Specified Currency
         other than U.S. dollars  ("Foreign  Currency  Notes") will be issued in




         authorized denominations that are equivalent,  at the 11:00 a.m. buying
         rate in the City of New York for  cable  transfers  in  such  Specified
         Currency as certified for customs purposes by the Federal  Reserve Bank
         of New York (the "Market Exchange  Agent") on the first Business Day in
         the  City of  New York  and  the country  issuing  such  currency  next
         preceding  the date  on which the Company accepts the offer to purchase
         such Foreign Currency Note, to $100,000  (rounded  down to  an integral
         multiple of  10,000  units  of  such  Specified  Currency) and integral
         multiples of 10,000 units of such Specified Currency in excess thereof.

                  (xiii) Any  legends to be  stamped  or  imprinted  on all or a
         portion of the Series B Notes, and the terms and conditions  upon which
         any legends may be removed, shall be as set forth in the form of Series
         B Notes.

                  (xiv)  If agreed by the initial purchaser and on behalf of the
         Company  by an  Authorized  Officer and set forth in an  Authentication
         Request,  any of the  Series  B Notes  shall  be issued  upon  original
         issuance as Book-Entry Notes. The Depository with respect to Book-Entry
         Notes shall be The Depository  Trust Company.  Any such Book-Entry Note
         may be exchanged  for Series B Notes registered in the name of a Holder
         other than the  Depository  or its nominee  only if (i) the  Depository
         notifies  the Company  that it is unwilling  or unable to  continue as
         Depository or the Depository ceases to be a clearing agency  registered
         under the  Securities  Exchange Act of 1934, as amended (the  "Exchange
         Act"),  (ii) the Company in its sole  discretion instructs  the Trustee
         that such Book-Entry Note shall be so exchangeable or (iii) there shall
         have occurred  and be  continuing an  Event of  Default with respect to
         such Book-Entry Note.

                  (xv)   The provisions of  Sections  10.1(B) and 10.1(C) of the
         Second Senior  Indenture relating to defeasance and discharge  prior to
         maturity are applicable to the Series B Notes; and further

                  RESOLVED,  that the form,  terms and  provisions  of the Third
         Supplemental  Indenture  to be dated as of August  1,1997  between  the
         Company  and the  Trustee  relating to the Series A Notes and the form,
         terms and provisions of the Fourth  Supplemental  Indenture to be dated
         as of September  30, 1998 between the Company and the Trustee  relating
         to the Series B Notes,  each in the form  presented to this meeting and
         supplementing  and amending the Second  Senior  Indenture,  be and they
         hereby are authorized and approved; and further

                  RESOLVED,  that the Authorized Officers be and they hereby are
         authorized,  for, in the name and on behalf of the Company, to execute,
         acknowledge and deliver the Third Supplemental Indenture and the Fourth
         Supplemental  Indenture  with such  changes  therein as the  Authorized
         Officers  executing  the  same  shall  approve,  such  approval  to  be
         conclusively   evidenced  by  such  officers'  execution  and  delivery
         thereof; and further




                  RESOLVED,  that the Authorized Officers be and they hereby are
         authorized for, in the name and on behalf of the Company, to enter into
         a  distribution  agreement  for the Series B Notes  (the  "Distribution
         Agreement")  with an investment  banking firm or firms or broker-dealer
         or  broker-dealers  as an agent or  agents  (the  "Note  Agents")  that
         authorizes,  among  other  things,  (i) the Note  Agents  to use  their
         reasonable efforts to solicit purchases of the Series B Notes, (ii) the
         purchase of the Series B Notes by the Note Agents  acting as  principal
         or (iii) a firm  underwriting  of the sale of the Series B Notes by the
         Note Agents,  such Distribution  Agreement to be in such form as may be
         approved by an Authorized  Officer,  such  approval to be  conclusively
         evidenced by such officer's execution and delivery thereof; and further

                  RESOLVED,  that any Authorized Officer is authorized to select
         one or more  investment  banking firms or  broker-dealers  ("Additional
         Agents")  in  addition  to the Note Agents to perform any or all of the
         duties and  obligations  specified in the  preceding  resolution,  upon
         written  agreement  in such form as may be  approved  by an  Authorized
         Officer,  with such  Authorized  Officer's  approval to be conclusively
         evidenced by his execution and delivery thereof; and further

                  RESOLVED, that notwithstanding the provisions of the preceding
         resolutions  relating to the execution of a Distribution  Agreement and
         the appointment of one or more Note Agents and Additional  Agents,  the
         Company reserves the right:

                  (i)    on its own behalf; to sell the Series B Notes  directly
         from time to time, in which event no  commissions  will be owed or paid
         in connection therewith;

                  (ii)   to  sell  the  Series  B  Notes  through  any member or
         members  of  a  group  comprised  of  one or more Note  Agents  and any
         Additional  Agents  to  the  exclusion  of  any  other  Note  Agents or
         Additional Agents and in such event no commission or other remuneration
         shall be owed to the latter Note Agents or Additional Agents; and

                  (iii)  to accept  or reject offers to purchase Series B Notes,
         in whole or in part; and further

                  RESOLVED,  that prior to sale of the Series B Notes, from time
         to time and subject to the terms of the preceding resolutions, any duly
         Authorized Officer shall on behalf of the Company have the authority to
         determine:

                  (i)    the aggregate  principal  amount  and maturities of the
         Series B  Notes to  be offered and  the initial  offering  price of the
         Series B Notes;

                  (ii)   whether such Series B Notes are to be Fixed Rate Notes,
         Floating Rate Notes or OID Notes  (including  zero coupon  obligations)
         and,  if  interest  bearing,  appropriate  Interest  Record  Dates  and
         Interest  Payment Dates and, if OID Notes,  appropriate  discount rates
         with respect thereto;





                  (iii)  whether  the Series  B Notes are to be Indexed Notes or
         Amortizing Notes;

                  (iv)   whether  the  Series  B  Notes  are  to  be  subject to
         redemption  at  the  option  of  the  Company and the terms thereof; if
         subject to redemption;

                  (v)    whether the Series B Notes will be subject to repayment
         by the  Company at  the option  of the  Holders thereof   prior  to the
         stated  maturity  of  the  Series  B  Notes,  and  the  terms  thereof,
         including, without limitation, designating Optional Repayment Dates;

                  (vi)   the  amount of any discounts, allowances or commissions
         to  be paid or allowed to the Note Agents and to any Additional Agents;
         and

                  (vii)  any  other  terms  of the  Series  B  Notes  and of the
         offering and sale thereof that are not  inconsistent  with this and the
         preceding resolutions;

         and  thereafter  to  cause an  appropriate  Prospectus  Supplement  and
         appropriate  Pricing  Supplements  to the  Prospectus  contained in the
         Second Registration Statement to be prepared, filed with the Commission
         and delivered to investors and one or more  Authentication  Requests to
         be delivered to the Trustee for action in keeping therewith.