  In the previous paper, we describe the intersection complexes of a toric
variety as a finite complex of graded exterior modules on the associated fan.
In this second part, we rewrite it explicitly by the barycentric subdivision of
the fan. We get the decomposition theorem of the intersection homologies for a
barycentric subdivision of a fan in the case of middle perversity. We get also
the diagonal theorems I and II. These theorems give a new proof of the
g-comnjecture on a simplicial polytope which was proved by R. Stanley.
