Throughout this paper, all groups are , nite. For a group G, we write Irr(G) for the set of irreducible characters of G. In this paper, we present a new characterization of GVZ-groups. A group G is a GVZ-group if every irreducible character ,2 Irr(G) satis, es that ,vanishes on G n Z( , ). The term GVZ-group was introduced by Nenciu in [12]. Nenciu continued the study of GVZ-groups in [13] and the second author further continued these studies in [10]. In our paper [2], we showed that GVZ-groups can be characterized in terms of another class of groups that have appeared in the literature. . .