Let G be a finite group and let NG denote the set of all non- trivial proper subgroups of G. A member K of NG is called n-decomposable if K is the union of n distinct conjugacy classes of G. The group G is called n-decomposable if and every member of NG is n-decomposable. In this paper we investigate the structure of n-decomposable finite groups for and classify them in the class of finite non-perfect groups.