This paper presents an output arbitrator for input buffering ATM (Asynchronous Transfer Mode) switches using neural networks. To avoid blocking in ATM switches with blocking characteristics, it is required to buffer ATM cells in input buffer and to schedule them. The N$ imes$N request matrix is divided into N/16 submatrices in order to get rid of internal blocking systematically in scheduling phase. The submatrices are grouped into N/4 groups, and the cells in each group are switched alternatively. As the window size of input buffer is increases, the number of input cells switched in a time slot approaches to N. The selection of nonblocking cells to be switched is done by neural network modules. N/4 neural network modules are operated simultaneously. Fast selection can be achieved by massive parallelism of neural networks. The neural networks have 4N neurons and 14N connection. The proposed method is implemented in C language, and the simulation result confirms the feasibility of this method