A module M is called H-co nitely supplemented if for every co nite submodule E (i.e. M=E is nitely generated) of M there exists a direct summand D of M such that M = E+X holds if and only if M = D+X, for every submodule X of M. In this paper we study factors, direct summands and direct sums of H-co nitely supplemented modules. Let M be an H-co nitely supplemented module and let N M be a submodule. Suppose that for every direct summand K of M, (N + K)=N lies above a direct summand of M=N. Then M=N is H-co nitely supplemented. Let M be an H-co nitely supplemented module. Let N be a direct summand of M. Suppose that for every direct summand K of M with M = N + K, N \ K is also a direct summand of M. Then N is H-co nitely supplemented. Let M = M1M2. If M1 is radical M2-projective (or M2 is radical M1-projective) and M1 and M2 are H-co nitely supplemented, then M is H-co nitely supplemented
