Rim, C.S.Naclerio, N.J.Masuda, SumioNakajima, K.Suppose that two sets of terminals t_l,t_2,...,t_n and b_1,b_2,...,b_n are located on two concentric circles C_out and C_in, respectively. Given a permutation PI of integers 1,2,...,n, the circular permutation layout problem is the problem of connecting each pair of terminals t_i and b_PI(i) for i = 1,2,. . .,n with zero width wires in such a way that no two wires which correspond to different terminal pairs intersect each other. In this paper, we present a linear time algorithm for the following case: (i) no wire can cross C_out, (ii) at most one wire can pass between any two adjacent terminals on C_in, and (iii) no wire can cross C_in more than once. The previously known algorithm for the same case has time complexity O(n^2).en-USTechnical Report