The generalized Hardie-Jansen product and its dual are defined and the fundamental results on these products are obtained. By studying the adjoint maps, we give proofs to them. Moreover we characterize the generalized Hardie-jansen product making use of the ${Gamma}W$-Whitehead product. We also obtain a characterization of the dual of the generalized Hardie-Jansen product using $({Gamma}W)$-Whitehead product.