- - - Department of Mathematics, Faculty of Mathematical and Computer Science, Kharazmi University, ۵۰ Taleghani Avenue, ۱۵۶۱۸ Tehran, Iran

Let A be a Banach algebra and X be an arbitrary Banach A-module. In this paper, we study the second transpose of derivations with value in dual Banach A-module X^{*}. Indeed, for a continuous derivation D:A\longrightarrow X^{*} we obtain a necessary and sufficient condition such that the bounded linear map \Lambda\circ D^{\prime\prime}:A^{**}\longrightarrow X^{***} to be a derivation, where \Lambda is composition of restriction and canonical injection maps. This characterization generalizes some well known results in [۲].

Derivation, second transpose, Banach module, module actions