A periodic sorter is a sorting network which is a cascade of a number of identical blocks, where output i of each block is input i of the next block. Previously, Dowd-Perl-Rudolph-Saks [5, 6] introduced by balanced merging network, with N =2k inputs/ outputs and logN stages of comparators. Using an intricate proof, they showed that a cascade of logN such blocks constitutes a sorting network. Recently (SPAA'93), we introduced a class of merging networks with N = 2k inputs/outputs and with periodic property . In this paper, we extend our class of merging networks to arbitrary size N. For each N, the class contains an exponentially large number of merging networks (about 2N/2-1) with [log N] stages.