In this paper, we extend earlier Michael’s selection theorem in the general nonconvex setting. Indeed, we deal with the case of almost lower semicontinuous multifunctions $T$ on a zero-dimensional paracompact topological space $X$. Based on a kind of equicontinuous property, we prove that any a.l.s.c. ECP multifunction from $X$ into a complete metric space $Y$ still has a continuous selection.