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

CERTIFICATION

I, William E. Hantke, Chief Financial Officer of The Premcor Refining Group Inc.
(the "Company"), pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, do
hereby certify as follows with respect to the Company:

     1.  The quarterly report on Form 10-Q of the Company for the period ended
         June 30, 2003, 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 such Form 10-Q fairly presents, in all
         material respects, the financial condition and results of operations of
         the Company.

         IN WITNESS WHEREOF, I have executed this Certification on this 25th day
of July, 2003.

                                                    By: /s/ William E. Hantke
                                                        ------------------------
                                                        Chief Financial Officer

A signed original of this written statement required by Section 906 has been
provided to The Premcor Refining Group Inc. and will be retained by The Premcor
Refining Group Inc. and furnished to the Securities and Exchange Commission or
its staff upon request.