1. In a cross-bar type asynchronous transfer mode switch, a method for arbitrating two or more competing output requests directed to the same output port, comprising the steps of: carrying out NAND operations between request signals for said output requests and one bit signals stored beforehand in a matrix, said matrix comprising a plurality of rows and a plurality of columns. for each row of said matrix; carrying out wired OR operations on the results of said NAND operation for each column of said matrix to obtain internal signal Q; detecting the complementary relationship between the order of the internal signal Q and the order on one row of said one bit signals stored beforehand in matrix form; and generating an acknowledgment signal for said output request for said row detected on said detecting step.