Bene? networks are known to be nonblocking rearrangeable networks which can realize arbitrary permutations. Topological equivalence extends the nonblocking rearrangeability to a class of multistage interconnection net-works (MIN), which has the same topology as Bene? networks.There is another class of well-known multistage interconnection networks, which is not yet known as either nonblocking rearrangeable networks or blocking networks, such as omega+omega networks. In this paper, we extends the labeling scheme used in Bene?-equivalent networks to a class of concatenated omega networks with modified central stage connection. The class of concatenated omega networks are proved to be nonblocking rearrangeable. A looping algorithm is proposed to routing through the networks to realize arbitrary permutation for the whole class of 2log2 N stage networks.