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

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... ities. The present method solves a class of very general models exactly. Few more problems are discussed as an application of this unitary transform method.