设G是任意群，本文给出了G-集G／H-分次模的分次自同态环的刻画．特别地，对我们证得N（H）／H-分次自同态环END（G／H，R）－gr（M）等于分次环ENDR（M）N（H）／H.

Let G be a group, H G. In this paper we shall give the characteristic of thegraded endomorphism ring with respect to a G-set G/H graded module. In particular,for a G-graded R-module M we obtain that the N(H)/H-graded endomorphism ringEND(G/H,R)-gr(M) equals the graded ring ENDR(M)N(H)/H.