Let M be a module over a ring R. We call M, γ -H-supplemented provided for every submodule N of M there is a direct summand D of M such that M = N + X if and only if M = D+ X for every submodule X of M with M/X noncosingular.We prove that M is γ -H-supplemented if and only if for every submodule N of M there exists a direct summand D of M such that (N +D)/N γ M/N and (N +D)/D γ M/D.
