An N × N Benes network B( n) ( n = log 2 N), being a rearrangeable network, can realize any N × N permutation in a single pass. But even in the presence of a single switch fault in B( n), two passes are necessary to realize any N × N permutation. In this paper, we attempt to characterize the switch fault sets in B( n), in the presence of which the network is always capable of realizing any arbitrary N × N permutation P in two passes, such that every source-destination connection is set up in a single pass, i.e., no recirculation is needed, but the whole set of N source-destination connections of P is partitioned in two subsets and are realized in two successive passes. An algorithm has been developed to test if the faulty B( n) is capable of realizing any arbitrary permutation in two passes by our technique; if it is yes, another algorithm also has been presented that computes the fault-tolerant routing to realize any arbitrary permutation P in two passes, through the faulty B( n). Finally, for this routing technique, the exact locations of the faults are not important, only the information of some optimal regions around the fault is sufficient. This feature actually enables us to develop very fast and simple procedures for identification of faulty regions of B( n), in the presence of multiple switch faults. Therefore, this fault-tolerant routing scheme enables us to make B( n) fault-tolerant in the presence of an easily-testable class of multiple switch faults, without any recirculation through intermediate nodes, or any reconfiguration of the system.