Abstract: Let (R,m,k) be Cohen-Macaulay local ring and M,N be finitely generated R modules. Let N∈ΩCM(R) and Ext1≤i≤dR(M,N)=0. We prove that HomR(M,N)∈ΩCM(R) and give some  conditions that the finitely generated module N is  the canonical module.

Key words: Cohen-Macaulay local ring, maximal Cohen-Macaulay module, canonical module