In this paper we give a combinatorial rule to compute the composition of two convolution products of endomorphisms of a free associative algebra and deduce the construction of a subalgebra of QBn(the group algebra of Hyperoctahedral group) which contains the descent algebra X#„. We also deduce a proof of the multiplication rule in the algebra ∑QBn- Finally, we generalize this construction to other wreath products of symmetric groups by abelian groups.