Let f be a transcendental meromorphic function of finite order with finitely many poles, c ∈ C\{0} and n, k ∈ N. Suppose f n(z) − Q1(z) and ( f n(z + c))(k) − Q2(z) share (0, 1) and f (z), f (z + c) share 0 CM. If n ≥ k + 1, then ( f n(z + c))(k) ≡ Q2(z)Q1(z) f n(z), where Q1, Q2 are polynomials with Q1Q2 . 0. Furthermore, if Q1 = Q2, then f (z) = c1e λ n z, where c1 and λ are non-zero constants such that eλc = 1 and λk = 1. Also we exhibit some examples to show that the conditions of our result are the best possible,