J. VUKMAN [6, Theorem 1] proved that if R is a prime ring of characteristic different from two and if d is a derivation of R such that [[d(x), x], x] = 0 for all x in R then either d = 0 or R is commutative. This is result extends one due to E. POSNER [5, Theorem 2]. In this paper our object is to generalize the above mentioned result of J. VUKMAN to Lie ideals and we prove the following: Theorem. Let R be a prime ring of characteristic different from two, and let d be a derivation of R. Let U be a Lie ideal of R such th at [[d(u), u], u] = 0 for all u is-an-element-of U. Then either d = 0 or U subset-of Z, where Z is the center of R.