A morphism of intersection homology induced by an algebraic map

Let $f:X \rightarrow Y$ be a map of algebraic varieties. Barthel, Brasselet, Fieseler, Gabber and Kaup have shown that there exists a homomorphism of intersection homology groups $f^{*}:IH^{*}(Y)\rightarrow IH^{*}(X)$ compatible with the induced homomorphism on cohomology. The crucial point in the argument is reduction to the finite characteristic. We give an alternative and short proof of the existence of a homomorphism $f^{*}$. Our construction is an easy application of the Decomposition Theorem.