Banyaga and Hurtubise defined the Morse–Bott–Smale chain complex as a quotient of a large chain complex by introducing five degeneracy relations. However, their five degeneracy relations are in fact redundant. In the present paper, we unify these five conditions into a single degeneracy condition and resolve the issue of the well-definedness of the Morse–Bott–Smale chain complex. This provides an appropriate definition of the Morse–Bott homology and more computable examples. Moreover, we show that our chain complex for a Morse–Smale function is quasi-isomorphic to the usual Morse–Smale–Witten chain complex. As a consequence, we obtain an alternative proof of the Morse Homology Theorem.