N-CSR Item 12(b) - Exhibits: Certifications

                            SECTION 906 CERTIFICATION

Pursuant to 18 U.S.C.ss.  1350, the  undersigned  officers of Federated  Premier
Municipal  Income Fund (the  "Registrant"),  hereby certify,  to the best of our
knowledge,  that the  Registrant's  Report on Form  N-CSR for the  period  ended
November 30, 2004 (the "Report") fully complies with the requirements of Section
13(a) or 15(d),  as  applicable,  of the Securities and Exchange Act of 1934 and
that the information  contained in the Report fairly  presents,  in all material
respects, the financial condition and results of operations of the Registrant.


Dated: August 15, 2005

/s/ J. Christopher Donahue

Title: President, Principal Executive Officer



Dated: August 15, 2005

/s/ Richard J. Thomas

Title: Treasurer, Principal Financial Officer

This  certification is being furnished solely pursuant to 18 U.S.C.ss.  1350 and
is not being filed as part of the Report or as a separate disclosure document.