We show that a non-elementary Möbius group acting in higher dimensions is discrete if and only if its elementary subgroup whose elements fix every limit point is finite and every two-generator subgroup is discrete. This result gives an improvement over earlier results of Abikoff and Haas [1], Fang and Nai [5], Martin [11] and the author [9]. We also give an example to show that the first condition is necessary when dimension $n\ge 3$.