  We consider a possibility of the existence of intersection homology morphism,
which would be associated to a map of analytic varieties. We assume that the
map is an inclusion of codimension one. Then the existence of a morphism
follows from Saito's decomposition theorem. For varieties with conical
singularities we show, that the existence of intersection homology morphism is
exactly equivalent to the validity of Hard Lefschetz Theorem for links. For
varieties with arbitrary analytic singularities we extract a remarkable
property, which we call Local Hard Lefschetz.
