THIRD SUPPLEMENTAL INDENTURE

                         dated as of September 29, 1998

                                      among

                            DRESSER INDUSTRIES, INC.
                           (as Issuer and Guarantor),

                              HALLIBURTON COMPANY,
                                 (as Guarantor)

                                       and

                    CHASE BANK OF TEXAS, NATIONAL ASSOCIATION
                                  (as Trustee)











(Baroid Note Indenture)





         This Third  Supplemental  Indenture  dated as of September  29, 1998 is
among Dresser  Industries,  Inc., a corporation  incorporated and existing under
the  laws  of  the  State  of  Delaware  ("Dresser"),   Halliburton  Company,  a
corporation  incorporated  and existing  under the laws of the State of Delaware
(the "Guarantor"), and Chase Bank of Texas, National Association (formerly Texas
Commerce Bank National Association),  a national banking association, as trustee
(the "Trustee").

                                    RECITALS:

         Baroid  Corporation,  a corporation  incorporated under the laws of the
State of Delaware  ("Baroid"),  duly  authorized  the  creation of its 8% Senior
Notes  due  2003  (the  "Securities")  and the  execution  and  delivery  of the
Indenture  dated as of April  22,  1993  between  Baroid  and the  Trustee  (the
"Original  Indenture")  and  issued  the  Securities  pursuant  to the  Original
Indenture.

         Following the acquisition of Baroid by Dresser, Baroid, Dresser and the
Trustee, thereunto duly authorized,  entered into a Supplemental Indenture dated
as of August 4, 1994 (the  "First  Supplemental  Indenture")  pursuant to which,
among other things, Dresser fully and unconditionally  guaranteed the payment of
the  principal,  premium,  if  any,  and  interest  on the  Securities  and  the
performance of Baroid's obligations under the Original Indenture.

         On October 30, 1997, Baroid was liquidated through  distribution of its
assets to and assumption of its liabilities by Dresser and was dissolved through
the  filing of a  Certificate  of  Dissolution  with the  Secretary  of State of
Delaware.

         As of  October  30,  1997,  Dresser  and the  Trustee,  thereunto  duly
authorized,   entered  into  a  Second   Supplemental   Indenture  (the  "Second
Supplemental  Indenture") pursuant to which Dresser assumed and succeeded to all
of  Baroid's   obligations   under  the  Original   Indenture,   as  theretofore
supplemented.

         On  September  29, 1998, a wholly  owned  subsidiary  of the  Guarantor
merged  with and into  Dresser as a result of which  Dresser,  as the  surviving
corporation, became a wholly owned subsidiary of the Guarantor.

         The Guarantor has duly authorized the full and unconditional  guarantee
of the Securities on the terms hereinafter set forth and has duly authorized the
execution and delivery of this Third Supplemental Indenture.

         Each of Dresser and the Trustee has duly  authorized  the execution and
delivery of this Third Supplemental Indenture.

         NOW, THEREFORE,  in consideration of the premises, the covenants herein
contained and other good and valuable consideration, the receipt and sufficiency
of which are hereby  acknowledged  by the parties  hereto,  the  parties  hereto
covenant and agree as follows:




                                   ARTICLE I.

         Section 1.01.  Definitions.  As used hereinafter:

                  (a)  the  term   "Indenture"   shall  mean  the  Indenture  as
         supplemented by the First, Second and Third Supplemental Indentures.

                  (b)  the term "Guarantor"  shall mean Halliburton  Company,  a
         Delaware corporation, and its successors and assigns.

         Section 1.02. Other  capitalized  terms used but not defined herein are
defined in the Original Indenture or the First or Second Supplemental  Indenture
and are used herein with the meanings ascribed to them therein.

                                   ARTICLE II.

         Section  2.01.  Amendment  of Article  10.  Article 10 of the  Original
Indenture,  as supplemented by the First  Supplemental  Indenture and the Second
Supplemental  Indenture,  is hereby amended so as to be and read in its entirety
as follows:

                                   ARTICLE 10

                             GUARANTEE OF SECURITIES

                  SECTION  10.01  Guarantee.  The  Guarantor  for  consideration
         received   unconditionally   and   irrevocably   guarantees   to   each
         Securityholder  (i) the due and punctual  payment of the  principal of,
         premium,  if any,  and interest on such  Security  when and as the same
         shall become due and payable,  whether at Stated Maturity,  as a result
         of  redemption,  upon exercise by the Holder of the  repurchase  option
         upon a Change of Control,  by acceleration  or otherwise;  (ii) the due
         and punctual  payment of interest on overdue  principal of and interest
         on the  Securities,  to the extent  lawful;  (iii) the due and punctual
         performance  of all  other  obligations  under  this  Indenture  to the
         Securityholders  or the  Trustee in  accordance  with the terms of such
         Security and of this  Indenture;  and (iv) in the case of any extension
         of time of  payment  or  renewal  of any  Securities  or any such other
         obligations,  that the same will be  promptly  paid in full when due or
         performed in accordance with the terms of the extension or renewal,  at
         Stated  Maturity,  at  redemption,  upon  exercise by the Holder of the
         repurchase  option  upon  a  Change  of  Control,  by  acceleration  or
         otherwise, to be paid by such Guarantor. In all respects, the Guarantor
         hereby  agrees that its  obligations  hereunder  shall be absolute  and
         unconditional,  irrespective  of,  and  shall  be  unaffected  by,  any
         invalidity,  irregularity or  unenforceability  of any such Security or
         any  other  Article  of this  Indenture,  any  failure  to  enforce  or
         exercise,  or delay in enforcing  or  exercising,  any right,  power or
         privilege  or any of the  other  provisions  of such  Security  or this
         Indenture,  any  waiver,  modification  or  indulgence  granted  to the
         Company with respect thereto by the  Securityholders or the Trustee, or
         any other  circumstances  which  may  otherwise  constitute  a legal or
         equitable  discharge  of a surety or  guarantor.  This  Guarantee  is a
         guarantee  of  payment  and not of  collection.  The  Guarantor  waives
         diligence,  presentment,  filing of claims with a court in the event of



         merger or bankruptcy of the Company,  any right to require a proceeding
         or demand first against the Company, the benefit of discussion, protest
         or  notice  with  respect  to any  such  Security  or the  indebtedness
         represented  thereby and all other  demands  whatsoever,  and covenants
         that this Guarantee will not be discharged as to any Security except by
         payment in full of the amount of principal  thereof,  premium,  if any,
         and interest  thereon and as provided by this Indenture.  The Guarantor
         further  agrees that, as between  Guarantor,  on the one hand,  and the
         Securityholders and the Trustee, on the other hand, (i) the maturity of
         the  obligations  guaranteed  hereby may be  accelerated as provided in
         Article 5 hereof for the  purposes of this  Guarantee,  notwithstanding
         any stay, injunction or other prohibition  preventing such acceleration
         in respect of the obligations  guaranteed hereby, and (ii) in the event
         of any  acceleration  of such  obligations  as  provided  in  Article 5
         hereof,  such  obligations  (whether  or not  due  and  payable)  shall
         forthwith  become due and payable by the  Guarantor  for the purpose of
         this Guarantee. In addition, without limiting the foregoing provisions,
         upon the effectiveness of an acceleration  under Article 5, the Trustee
         shall  promptly make a demand for payment on the  Securities  under the
         Guarantee provided for in this Article 10 and not discharged;  provided
         that the  failure  by the  Trustee  to make any such  demand  shall not
         impair or otherwise affect the obligations of the Guarantor.

                  The  Guarantee  set forth in this  Section  10.01 shall not be
         valid or become obligatory for any purpose with respect to any Security
         unless the certificate of authentication  shall have been signed by the
         Trustee.

                  The obligations of Guarantor  pursuant to this Guarantee shall
         continue to be effective or automatically  reinstated,  as the case may
         be, if at any time  payment  of  obligations  under this  Indenture  is
         rescinded  or  otherwise   must  be  restored  or  returned   upon  the
         insolvency, bankruptcy,  dissolution,  liquidation or reorganization of
         the  Company or the  Guarantor  or for any  reason,  all as though such
         payment had not been made.

                  The  Guarantor  shall  be  subrogated  to  all  rights  of the
         Securityholders and the Trustee under the Securities and the Indenture;
         provided,  however,  that the  Guarantor  shall not be  entitled to any
         payments arising out of such subrogation  right until the principal of,
         premium,  if any,  and  interest  on all  Securities  shall  have  been
         irrevocably  paid  in  full  in  accordance  with  the  terms  of  such
         Securities, the Indenture and the Guarantee.

                  To the extent that any right,  power or authority is available
         under this  Indenture to the Trustee or any  Securityholder  to enforce
         the provisions of the Securities,  the Trustee and each  Securityholder
         shall have all such rights, powers and authority, not inconsistent with
         the express  provisions  of this  Guarantee,  necessary  to enforce the
         provisions  of this  Guarantee.  Each and every  default  to which this
         Guarantee  applies  shall  give  rise to a  separate  cause  of  action
         hereunder, and separate suits may be brought hereunder as each cause of
         action arises.  No remedy  conferred upon or reserved to the Trustee or
         any  Securityholder  is intended to be exclusive of any other remedy or
         remedies, but each and every remedy shall be cumulative and shall be in
         addition to every other remedy given under this Guarantee either now or
         hereafter existing at law or in equity.




                  SECTION 10.02 Obligations of Guarantor Unconditional.  Nothing
         contained in this  Article 10 or elsewhere in this  Indenture or in any
         Security is intended to or shall impair, as between  Guarantor,  on one
         hand,  and the  Trustee  and the  Securityholders,  on the  other,  the
         obligation of Guarantor, which is absolute and unconditional, to pay to
         the  Securityholders and the Trustee the principal of, premium, if any,
         and  interest on the  Securities  as and when the same shall become due
         and payable in accordance  with the provisions of this  Guarantee,  nor
         shall   anything   herein  or  therein   prevent  the  Trustee  or  any
         Securityholder  from  exercising  all remedies  otherwise  permitted by
         applicable law upon an Event of Default under this Indenture.

                  SECTION  10.03   Execution  of  Guarantee.   To  evidence  its
         guarantee to the Securityholders and the Trustee,  the Guarantor hereby
         agrees to execute a notation relating to the guarantee on each Security
         authenticated   and  made  available   after  the  date  of  the  Third
         Supplemental  Indenture for delivery by the Trustee.  Such notation may
         take  the  form of the  Guaranty  attached  to the  Third  Supplemental
         Indenture as Annex A. The  Guarantor  hereby  agrees that its Guarantee
         set  forth in  Section  10.01  shall  remain in full  force and  effect
         notwithstanding  any failure to endorse on each  Security a notation of
         such Guarantee.

                                  ARTICLE III.

         Section 3.01.  Effectiveness.  This Third Supplemental Indenture shall,
upon execution and delivery hereof by all the parties hereto,  become  effective
as of  the  date  hereof.  From  and  after  the  effectiveness  of  this  Third
Supplemental  Indenture,  the  Indenture,  as hereby  supplemented,  amended and
modified, shall remain in full force and effect.

         Section 3.02. References. Each reference in the Indenture or this Third
Supplemental  Indenture  to any  article,  section,  term  or  provision  of the
Indenture  shall mean and be deemed to refer to such article,  section,  term or
provision of the Indenture,  as modified by this Third  Supplemental  Indenture,
except where the context otherwise indicates.

         Section 3.03. Benefit. All the covenants, provisions,  stipulations and
agreements  contained in this Third Supplemental  Indenture are and shall be for
the sole and  exclusive  benefit of the parties  hereto,  their  successors  and
assigns,  and of the  holders  and  registered  owners  from time to time of the
Securities issued and outstanding from time to time under the Indenture.

         Section 3.04.  Counterparts.  This Third Supplemental Indenture  may be
executed  in  any  number  of  counterparts,  each of  which shall be  deemed an
original  and  all  of  which  taken  together  shall be deemed to be a single
instrument.

         Section 3.05. Governing Law. This Third Supplemental Indenture shall be
deemed to be a  contract  under  the laws of the State of New York,  and for all
purposes  shall be construed in  accordance  with the laws of such state without
regard to principles  of conflicts of laws,  except as may otherwise be required
by mandatory provisions of law.



         Section 3.06.  Headings.  The Article and Section  headings herein are
for  convenience  only and shall not affect the construction hereof.

         IN WITNESS WHEREOF, the said Halliburton  Company,  Dresser Industries,
Inc. and Chase Bank of Texas,  National  Association have each caused this Third
Supplemental Indenture to be executed in its corporate name by the officer whose
name is subscribed below,  thereunto duly authorized,  and its corporate seal to
be  hereunto  affixed  and,  in the cases of  Halliburton  Company  and  Dresser
Industries,  Inc., attested by its Secretary or Assistant  Secretary,  all as of
the day and year first above written.

                                       HALLIBURTON COMPANY


                                       By  /s/ Lester L. Coleman
                                          -----------------------------
Attest:                                Name:   Lester L.  Coleman
                                       Title:  Executive Vice President
                                                and General Counsel


By  /s/ John M. Allen
   --------------------------
Name:   John M. Allen
Title:  Assistant Secretary


                                       DRESSER INDUSTRIES, INC.


                                       By  /s/ Lester L. Coleman
                                          ------------------------------
                                       Name:   Lester L. Coleman
Attest:                                Title:  Senior Vice President


By  /s/ John M. Allen
   --------------------------
Name:   John M. Allen
Title:  Assistant Secretary


                                       CHASE BANK OF TEXAS,
                                       NATIONAL ASSOCIATION


                                       By  /s/ Letha Glover
                                          ------------------------------
                                       Name:   Letha Glover
                                       Title:  Assistant Vice President and
                                                    Trust Officer






                                                                      ANNEX A


                                    GUARANTEE


         Halliburton  Company  (the  "Guarantor")  has,  pursuant  to the within
mentioned  Indenture,  unconditionally  guaranteed  that (a) the  principal  of,
premium,  if any,  and  interest  on the  Securities,  if lawful,  and all other
obligations of the Company to the Holders or the Trustee will be paid in full or
performed,  all in  accordance  with  the  terms  hereof  and set  forth  in the
Indenture, and (b) in the case of any extension of time of payment or renewal of
any Securities or any such other obligations,  the same will be promptly paid in
full when due or  performed  in  accordance  with the terms of the  extension or
renewal, at Stated Maturity,  at redemption,  by acceleration or otherwise.  The
Guarantee  will be binding upon the Guarantor and its successors and assigns and
will inure to the benefit of the  successors  and assigns of the Trustee and the
Holders and, in the event of any transfer or  assignment of rights by any Holder
or the  Trustee,  the  rights  and  privileges  conferred  upon that  party will
automatically  extend to and be  vested  in such  transferee  or  assignee,  all
subject to the terms and conditions  contained in the  Indenture.  The Guarantee
will not be valid or  obligatory  for any  purpose  with  respect  to a Security
unless the certificate of  authentication on the Security has been signed by the
Trustee.

                                       HALLIBURTON COMPANY



                                       By:  /s/ Lester L. Coleman
                                           -----------------------------
                                                Lester L.  Coleman
                                                Executive Vice President and
                                                      General Counsel