  An interacting spin-fermion model is exactly solved on an open chain. In a
certain representation, it is the nearest-neighbor Hubbard model in the limit
of infinite $U$ (local interaction). Exact solution of its complete energy
eigen-spectrum is accomplished by introducing a unitary transformation which
maps the original problem to a tight-binding model of the fermions only.
Physically, the exact solution implies the absence of Nagaoka ferromagnetism in
the ground state for arbitrary electron densities. The present method solves a
class of very general models exactly. Few more problems are discussed as an
application of this unitary transform method.
