  Let $S$ be a finite semigroup. In this paper we introduce the functions
$\phi_s:S^* \to S^*$, first defined by Rhodes, given by $\phi_s([a_1,a_2
,...,a_n]) = [sa_1,sa_1a_2,..., sa_1a_2 ... a_n]$. We show that if $S$ is a
finite aperiodic semigroup, then the semigroup generated by the functions
$\{\phi_s\}_{s \in S}$ is finite and aperiodic.
