- - - Department of Mathematics, Islamic Azad University, Garmsar Branch, Garmsar, Iran.

In this paper we study the module contractibility of Banach algebras and characterize them in terms the concepts splitting and admissibility of short exact sequences. Also we investigate module contractibility of Banach algebras with the concept of the module diagonal.

Banach algebra, Banach module, module derivation, module contractible, module diagonal