General solution of linear vector supersymmetry

We give the general solution of the Ward identity for the linear vector supersymmetry which characterizes all topological models. Such so- lution, whose expression is quite compact and simple, greatly simplifies the study of theories displaying a supersymmetric algebraic structure, reducing to a few lines the proof of their possible finiteness. In particular, the co- homology technology usually involved for the quantum extension of these theories, is completely bypassed. The case of Chern-Simons theory is taken as an example.