CERTIFICATION

R. Jay Gerken, Chief Executive Officer, and Kaprel Ozsolak, Chief Financial Officer of Municipal High Income Fund Inc. (the “Registrant”), each certify to the best of his knowledge that:

1. The Registrant’s periodic report on Form N-CSR for the period ended October 31, 2005 (the “Form N-CSR”) fully complies with the requirements of section 15(d) of the Securities Exchange Act of 1934, as amended; and

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

Chief Executive Officer
Municipal High Income Fund Inc.

/s/ R. Jay Gerken
R. Jay Gerken
Date: January 9, 2006

Chief Financial Officer
Municipal High Income Fund Inc.

/s/ Kaprel Ozsolak
Kaprel Ozsolak
Date: January 9, 2006

This certification is being furnished to the Securities and Exchange Commission solely pursuant to 18 U.S.C. § 1350 and is not being filed as part of the Form N-CSR with the Commission.