THIRD SUPPLEMENTAL INDENTURE

                           Dated as of August 1, 1997

                                     between

                               HALLIBURTON COMPANY

                                       and

                    TEXAS COMMERCE BANK NATIONAL ASSOCIATION

                                   as Trustee









(Second Senior Indenture)



                                TABLE OF CONTENTS

                                                                           Page


                                    ARTICLE I

DEFINITIONS


    Section 1.1  Definitions.............................................     1

                                   ARTICLE II

AMENDMENTS


    Section 2.1  Amendment of Section 2.1 of the
                 First Supplemental Indenture............................     2

                                   ARTICLE III


MISCELLANEOUS

    Section 3.1  Counterparts............................................     2
    Section 3.2  Effect of Headings.   ..................................     2
    Section 3.3  Provisions for the Sole Benefit of Parties and Holders..     2




                          THIRD SUPPLEMENTAL INDENTURE

         This Third Supplemental Indenture dated as of August 1, 1997 is between
Halliburton Company, a Delaware corporation ("Halliburton"),  and Texas Commerce
Bank National  Association,  a national  banking  association,  as Trustee,  and
amends and  supplements  that certain Second Senior  Indenture dated December 1,
1996 between  Halliburton  and the Trustee (the "Second Senior  Indenture"),  as
heretofore amended and supplemented by the First Supplemental Indenture dated as
of December 5, 1996 between Halliburton and the Trustee (the "First Supplemental
Indenture") and the Second Supplemental  Indenture dated as of December 12, 1996
among Halliburton,  Halliburton Hold Co., a Delaware corporation (the "Issuer"),
and  the  Trustee  (the  "Second  Supplemental   Indenture")(the  Second  Senior
Indenture,  as  heretofore  amended and  supplemented,  being herein  called the
"Indenture").

                                    RECITALS:

         Pursuant to the Second Senior Indenture, as amended and supplemented by
the First Supplemental Indenture, Halliburton, as the predecessor of the Issuer,
proposed to offer,  sell and issue from time to time,  at an  aggregate  initial
offering price of up to $300,000,000, certain notes of its series of medium-term
notes due nine months or more from date of issue.

         For that purpose,  Halliburton,  as the  predecessor of the Issuer,  by
means  of  the  First  Supplemental   Indenture,   established  such  series  of
medium-term  notes and certain terms and provisions  thereof that were different
from,  or in addition  to, those  provided in the Second  Senior  Indenture  and
acknowledged  that the remaining terms and provisions of such medium-term  notes
would be  established  pursuant to the  provisions  of Section 2.3 of the Second
Senior Indenture.

         Since  that  time,  the Issuer  has  offered,  sold and issued  various
medium-term  notes of such series for an  aggregate  initial  offering  price of
approximately  $300,000,000,  and,  consequently,  the Issuer has  determined to
increase the aggregate size of such series of medium-term  notes due nine months
or more from date of issue,  thereby making  available  additional notes of such
series for offering, sale and issuance.

         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

                                   DEFINITIONS

         Section  1.1  Definitions.  Capitalized  terms  used  but  not  defined
herein  are defined  in the  Indenture, including  without  limitation the First
Supplemental  Indenture,  and  are  used herein with the definitions ascribed to
them therein.



                                   ARTICLE II

                                   AMENDMENTS

         Section  2.1  Amendment  of  Section  2.1  of  the  First  Supplemental
Indenture.  Section 2.1 of the First Supplemental Indenture, as contained in the
Indenture, is hereby amended so as to be and read in its entirety as follows:

                  Section  2.1   Establishment   of  Series.   Pursuant  to  the
         provisions of Section 2.3 of the Indenture, there is hereby established
         a series of Securities  designated  generally as the Medium-Term  Notes
         Due Nine Months or More From Date of Issue,  Series A, that may be sold
         and issued from time to time, at an aggregate initial offering price of
         up to U. S.  $500,000,000  (the  "Notes"),  subject to reduction by the
         aggregate  initial  offering price of any other  Securities that may be
         theretofore  sold and issued by the Issuer pursuant to the terms of the
         Indenture.  Forms  of a Fixed  Rate  Note  and a  Floating  Rate  Note,
         excluding  in each case terms and  provisions  to be  included  therein
         pursuant to a Note Terms  Certificate,  are attached hereto as Exhibits
         B-1 and B-2, respectively, and by this reference incorporated herein.


                                   ARTICLE III

                                  MISCELLANEOUS

         Section 3.1  Counterparts.  This Third Supplemental  Indenture  may  be
executed  in  any  number  of  counterparts, each  of which  shall be  deemed an
original, but  all  of which  shall  together  constitute  but one and  the same
instrument.

         Section 3.2  Effect  of Headings.  The  Article and  Section   headings
herein  and in the  Table of Contents  are for convenience  only and  shall  not
affect the construction hereof.

         Section  3.3  Provisions  for the  Sole Benefit of Parties and Holders.
Nothing in the Indenture, as supplemented,  amended  and modified  by this Third
Supplemental  Indenture, or in the Notes, expressed or implied, shall give or be
construed  to give to any person,  firm or  corporation,  other than the parties
hereto and their  successors  and the  Holders,  any legal or  equitable  right,
remedy or claim under the Indenture,  as so supplemented,  amended and modified,
or under any covenant or provision  herein  contained,  all such  covenants  and
provisions being for the sole benefit of the parties hereto and their successors
and of the Holders.




         IN  WITNESS  WHEREOF,   the  parties  hereto  have  caused  this  Third
Supplemental  Indenture to be duly executed and the appropriate  corporate seals
to be hereunto affixed and attested, all as of the 1st day of August, 1997.



                                  HALLIBURTON COMPANY


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


Attest:


    /s/ Susan S. Keith
- --------------------------------------
Title:  Vice President and Secretary

                                  TEXAS COMMERCE BANK NATIONAL
                                          ASSOCIATION


                                  By:
                                     -------------------------------
                                  Title: