EXHIBIT 99.4
                                                                    ------------



    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 Annual Report of Precision Drilling Corporation
(the "Company") on Form 40-F for the year ended December 31, 2003, as filed with
the Securities and Exchange Commission on the date hereof (the "Report"), I,
Dale E. Tremblay, Senior Vice-President & 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 to the best of my knowledge:

1.   The Report fully complies with the requirements of section 13(a) or 15(d)
     of the Securities Exchange 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.


     By:  /s/ Dale E. Tremblay
          ---------------------------------
          Dale E. Tremblay
          Senior Vice-President & Chief Financial Officer


April 26, 2004