CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT

I, James A. Bowen,  Chief Executive  Officer of First Trust/Four  Corners Senior
Floating Rate Income Fund II (the "Registrant"), certify that:

     1.  The Form N-CSR of the Registrant (the "Report") fully complies with the
         requirements  of Section 13(a) or 15(d) of the Securities  Exchange Act
         of 1934, as amended; and

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

Date:    August 5, 2004                 /S/ James A. Bowen
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                                        James A. Bowen, Chief Executive Officer
                                        (principal executive officer)

I, Mark R. Bradley,  Chief Financial Officer of First Trust/Four  Corners Senior
Floating Rate Income Fund II (the "Registrant"), certify that:

     1.  The Form N-CSR of the Registrant (the "Report") fully complies with the
         requirements  of Section 13(a) or 15(d) of the Securities  Exchange Act
         of 1934, as amended; and

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

Date:    August 5, 2004                 /S/ Mark R. Bradley
     ----------------------             ----------------------------------------
                                        Mark R. Bradley, Chief Financial Officer
                                        (principal financial officer)