Banyaga and Hurtubise defined the Morse–Bott–Smale chain complex as a quotient of a large chain complex by introducing five degeneracy relations. In this paper, we unify the five conditions into only one degeneracy condition. This allows for a simpler definition of Morse–Bott homology and more computable examples. Moreover, we show that our chain complex for a Morse–Smale function is quasi-isomorphic to the Morse–Smale–Witten chain complex. As a result, we obtain another proof of the Morse Homology Theorem.