In this paper, for the single s-a-E fault detected in a triangular cellular permutation network (TCPN), we propose a method which can tolerate a fault by reconfiguring the netowrk and analyze the possibilities of the reconfiguration. The network is set up through iterative decomposition of a permutation into the right or left coset. For the s-a-E fault of a cell which is to be transpositioned for an increasing order mapping, we cna reconfigure it merely by switching te decomposition scheme from right coset to left coset or vice versa. Also for a decreasing order mapping, we make a detour around the faulty cell. Reconfiguring with the redundant connectivity of a TCPN, we could realize form 17% to 90% of the permutation for the number of inputs from 4 to 40. REconfiguration of the network by exchanging the first input with the last input and the first output with the last output resulted in more than 99% realization of the permutation. Also with the exchange of all inputs and outputs with neighboring cells, we could have 100% realization of the permutation.