CERTIFICATION PURSUANT TO RULE 30A-2(B) UNDER THE 1940 ACT AND
                     SECTION 906 OF THE SARBANES-OXLEY ACT

I, James A. Bowen, President of First Trust/Fiduciary Asset  Management  Covered
Call Fund (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:    FEBRUARY 24, 2005               /S/ JAMES A. BOWEN
     ----------------------          -------------------------------------------
                                     James A. Bowen, President
                                     (principal executive officer)

I, Mark R. Bradley, Chief Financial Officer of First Trust/Fiduciary Asset
Management Covered Call Fund (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:    FEBRUARY 24, 2005               /S/ MARK R. BRADLEY
     ----------------------          ----------------------------------------
                                     Mark R. Bradley, Chief Financial Officer
                                     (principal financial officer)