Suppose I=[0,1] and C°(I, I) denotes the set of all continuous mappings of the interval. Let f∈C°(I, I), P(f), Ω(f) and ent (f) denote the set of all periodic points of f, the nonwandering set of f and the topological entropy of f, respectively. Together with the results of Bowen-Franks (Topology, 15 (1976), 337—342) and Block (Proc. Amer. Math. Soc., 72 (1978), 576—580)7 recently the author has proved the following theorem.