We propose an ATM switch architecture using the multistage interconnection network based on the GAMMA network. Consisting of 3 x 3 crossbar switch elements, the GAMMA network provides multiple paths. For this reason, this switch can be constructed without any sorting network which is required for other space division ATM switches based on the delta or banyan networks in order to avoid internal blocking. Most of the space division switches deteriorate switch performance when internal switch elements or interconnection links fail because they only one path between input and ouput ports. The proposed switch, however, has reliabilty by providing multiple paths with the GAMMA network.This switch architecture has two network planes: the upper and lower plane. The upper plane is used for searching for the paths of the request cells, whearas the lower plane is used for routing the information cells. Since the switch can negotiate possible paths for next cell while one cell is routed through the lower plane, we can utilize the characteristics of the multiple paths in GAMMA network. Finally we show the performance of this switch by simulation.