EXHIBIT 32.2


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


In connection with the Quarterly Report of Halliburton Company (the "Company")
on Form 10-Q for the period ending September 30, 2003 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, pursuant to
18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley
Act of 2002, 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.


       /s/ C. Christopher Gaut
       -----------------------------
       C. Christopher Gaut
       Chief Financial Officer
       November 6, 2003