EXHIBIT 5

                          TRANSCANADA PIPELINES LIMITED

                              450 - 1st Street S.W.
                            Calgary, Alberta, Canada
                                     T2P 5H1

                    CERTIFICATION OF CHIEF FINANCIAL OFFICER
                 UNDER SECTION 906 OF SARBANES-OXLEY ACT 0F 2002

I, Russell K. Girling, the Chief Financial Officer of TransCanada PipeLines
Limited (the "Company"), in compliance with 18 U.S.C. Section 1350, as adopted
pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, hereby certify, in
connection with the Company's Annual Report as filed on Form 40-F for the fiscal
year ending December 31, 2003 with the Securities and Exchange Commission (the
"Report"), that:

     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.


                                      /s/ Russell K. Girling
                                      ------------------------------------------
                                      Russell K. Girling
                                      Chief Financial Officer
                                      March 15, 2004