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 t of the next block. Previously, Dowd-Perl-Rudolph-Saks [4, 5] introduced the balanced merging network, with N = 2inputs/outputs and log N stages of comparators. Using an intricate proof, they showed that a cascade of log N such blocks constitutes a sorting network. In this paper, we introduce a large class of merging networks with the same periodic property. This class contains 22 1 networks, where N = 2is the number of inputs. The balanced merger is one network in this class. Other networks use fewer comparators. We provide a Yery simple and elegant proof of periodicity, based on the recursive structure of the networks. Our construction can also be extended to arbitrary-sized networks (not necessarily a power of 2).