A well known theorem ([1] page 432) in the study of finite groups states that if P is a Sylow p-subgroup of the finite group G, and if P0 is a normal subgroup of P such that whenever two elements, σ and τ, of P are conjugate in G, the cosets σP0 and τP0 are conjugate in P/P0, then there is a normal subgroup K of G such that G = KP and K ∩ P = P0. In this note we will extend this result to allow P to be any Hall subgroup if G is solvable. More precisely, following theorem will be the proved.