Let H and G be two simple graphs. The concept of an H-magic decomposition of G arises from the combination between graph decomposition and graph labeling. A decomposition of a graph G into isomorphic copies of a graph H is H-magic if there is a bijection f: V (G)∪ E (G)→{1, 2,...,∣ V (G)∪ E (G)∣} such that the sum of labels of edges and vertices of each copy of H in the decomposition is constant. A lexicographic product of two graphs G 1 and G 2, denoted by G 1 [G 2], is a graph which arises from G 1 by replacing each vertex of G 1 by a copy of the G 2 and each edge of G 1 by all edges of the complete bipartite graph K n, n where n is the order of G 2. In this paper we provide a sufficient condition for in order to have a -magic decompositions, where n> 3, m> 1, and t= 3, 4, n− 2.