Let G and Γ be groups,a graded ring of type G with an identity, a graded ring of type Γ with an identity,R#G and A#Γsmash products of R and A, respectively. Let W=(_gU_(σ-1))_(g,σ)i.e. a set of all|G|》×|Γ| matrices whose element in the(g,σ)-position belongs to gU_(σ-1). Suppose each matrix in W only has finitely non zero elements.Then W is an(R#G,A#Γ)-bimodule with the matrix addition and multiplication and _RU_Adefines a graded Morita duality iff _(R#G)W_(A#Γ) defines a Morita duality.