For a permutation ${mu}$ in S$sub$b/, the limit algebra A${mu}$ of the stationary system given by ${mu}$ is isomorphic to a refinement limit algebra if and only if its exponent set E(${mu}$) is the set {0}. In the current paper, we prove a sufficient condition under which E(${mu}$)={0} when the order of ${mu}$ is a power of p, where p is a prime number dividing b.