With the property of simple structure, self-routing and low hardware complexity, Banyan networks has been taken as interconnection network by many multi-processor systems and switching systems. However, its blocking property limits its performance and wide use. It is known that Banyan network is nonblocking for some special input/output patterns. In this paper, a class of nonblocking property of Banyan network is discussed, then some useful examples are demonstrated through application to ATM switch design: to promote ability of load sharing through data distribution and to implement multicast ability using lower hardware cost.