Certification Pursuant to Rule 30a-2(b) under the 1940 Act and
                  Section 906 of the Sarbanes-Oxley Act

I, James A. Bowen, Chairman of the Board, President and Chief Executive Officer
of First Trust/Four Corners Senior Floating Rate Income 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: July 20, 2010

                                     /s/ James A. Bowen
                                     ----------------------------------------
                                     James A. Bowen, Chairman of the Board,
                                     President and Chief Executive Officer
                                     (principal executive officer)





I, Mark R. Bradley, Treasurer, Controller, Chief Financial Officer and
Chief Accounting Officer of First Trust/Four Corners Senior Floating Rate Income
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: July 20, 2010

                                     /s/ Mark R. Bradley
                                     ----------------------------------------
                                     Mark R. Bradley Treasurer, Controller,
                                     Chief Financial Officer and
                                     Chief Accounting Officer
                                     (principal financial officer)