  As a natural generalization of chromatic number of a graph, the circular
chromatic number of graphs (or the star chromatic number) was introduced by
A.Vince in 1988. Let $M^t(G)$ denote the $t$th iterated Mycielski graph of $G$.
It was conjectured by Chang, Huang and Zhu(Discrete mathematics,205(1999),
23-37) that for all $n \ge t+2, \chi_c(M^t(K_n))=\chi(M^t(K_n))=n+t.$ In 2004,
D.D.F. Liu proved the conjecture when $t\ge 2$, $n\ge 2^{t-1}+2t-2$. In this
paper,we show that the result can be strengthened to the following: if $t\ge
4$, $n\ge {11/12}2^{t-1}+2t+{1/3}$, then $\chi_c(M^t(K_n))=\chi(M^t(K_n))$.
