  Let G be a finite group. We study the group of G-equivariant self-homotopy
equivalences of product of G-spaces. For a product of n-spaces, we represent it
as product of n-subgroups under the assumption of equivariant reducibility.
Further we describe each factor as a split short exact sequence. Also, we
obtain an another kind of factorisation, called $LU$ type decomposition, as
product of two subgroups.
