We shall denote by $F$ the composition operator generated by a given function $f: {\bold R} \longrightarrow {\bold R}$. In this paper we prove that the composition operator $F$ maps the space $RV_p[a,b] (p > 1)$ into the space $BV[a,b]$ if and only if $f$ satisfies a local Lipschitz condition on {\bf R}.