  In this paper, we characterize a Rickard complex, which induces a Rickard
equivalence between the block algebras of a block $b$ and its Brauer
correspondent and whose vertices have the same order as defect groups of the
block $b$. The homology of such a Rickard complex vanishes at all degree but
degree $q$, and the homology at degree $q$ induces a basic Morita equivalence
between the block algebras in the sense of Puig.
