The results presented in this paper extend a dual version of the reflexivity theorem of W. Bade to locally convex spaces. Dual versión of the Bade theorem in a Banach C(K)-module was firstly discovered in [1]. It is our aim to extend it to a locally convex C(K)-module. As a consequence, it is proven that each unital w* operator topology closed subalgebra of the w* operator topology closed algebra generated by a Boolean algebra of projections is reflexive.