In this paper it is proved that if T is a bounded linear operator on a Hilbert space H and (W(T)),where cl(W(T)) is the closure of W(T) ={(Tx,x);x E H,11 x1l = 1},then T is normal iff Uj = (T-A)-1(T-A,) is hyponormal and T is hyponormal iff Uk= (T-A) (T-A
