Exascale computing systems are being built with thousands of nodes. A key component of these systems is the interconnection network. The high number of components significantly increases the probability of failure. If failures occur in the interconnection network, they may isolate a large fraction of the machine. For this reason, an efficient fault-tolerant mechanism is needed to keep the system interconnected, even in the presence of faults. A topology recently proposed for these large systems is the hybrid KNS family that provides good performance and connectivity at a reduced hardware cost. This paper present a fault-tolerant routing methodology for the KNS topology that degrades performance gracefully in the presence of faults and tolerates a reasonably large number of faults without disabling any healthy node. In order to tolerate network failures, the methodology uses a simple mechanism: for some sourcedestination pairs, only if necessary, packets are forwarded to the destination node through a set of intermediate nodes (without being ejected from the network) which allow avoiding faults. The evaluation results shows that the methodology tolerates a large number of faults. Furthermore, the methodology offers a gracious performance degradation. For instance, performance degrades only 1% for a 2D-network with 1024 nodes and 1% faulty links.