This paper proposes a multistage interconnection ATM switching network without internal blocking. The first is recirculating shuffle-exchange network improved on hardware complexity. The next is connected to Rank network with tree structure. In this network, after the packets transferred to the same output ports are given each priority, only a packet with highest priority is sent to the next, an the others are recirculated to the first. Rearrangeability through decomposition and composition algorithm is applied for the transferred packets in hanyan network and all they arrive at a final destinations. To analyze throughput, waiting time and packet loss ratio according tothe size of buffer, the probabilities are modeled by a binomial distribution of packet arrival.