  In this paper, firstly we investigate conditions under which the action of an
operator on a $K$-frame, remain again a $K$-frame for Hilbert module E. We also
give a generalization of Douglas Theorem and we shall use it to prove the sum
of two $K$-frame under certain condition is again a $K$-frame. Finally, we
characterize the $K$-frame generators for a unitary system in terms of
operators.
