CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350
                             AS ADOPTED PURSUANT TO
                  SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002



This  certification is provided pursuant to ss. 906 of the Sarbanes-Oxley Act of
2002, 18 U.S.C. ss. 1350, and accompanies the Annual Report on Form 10-K for the
period ended December 31, 2003 of Halliburton  Company (the  "Company") as filed
with the Securities and Exchange Commission on the date hereof (the "Report").

I, C. Christopher Gaut, Chief Financial Officer of the Company, certify that:

    (1)   The Report fully  complies with the  requirements of  section 13(a) or
          15(d) of the Securities Act of 1934; and

    (2)   The  information  contained  in  the Report fairly  presents,  in  all
          material   respects,   the   financial   condition  and   results   of
          operations of the Company.



------------------------------
C. Christopher Gaut
Chief Financial Officer
March 8, 2004