Abstract: Let be a nonempty set and be a binary relation of . A directed graph is a pair , where is the vertex set of and is a collection of ordered pair of the vertices , called arcs. That can be reached from or can reach means there is a directed path from to . A strongly connected digraph is one in which any vertex can be reached from any other vertex by a directed path. A tournament is a directed graph in which there is exactly one arc between any two vertices. A strongly connected tournament is called a strong tournament. In this paper we discuss the property of the strong tournament with at least four vertices and give out another proof of Moon theorem by the particular property.