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Fault tolerance in the interconnection network of large clusters of PCs is an issue of growing importance, since their increasing size also increases the failure probability. The fat-tree topology is usually used in these machines since it has become very popular among high-speed interconnect manufacturers. This paper proposes a new distributed fault-tolerant routing methodology for fat trees. Unlike other previous proposals, it does not require additional network hardware, and its memory requirements, switch hardware, and routing delay scales up with the network size. Indeed, it nullifies only the strictly necessary paths, allowing adaptive routing through the healthy paths. The methodology is based on enhancing the interval routing scheme with exclusion intervals. Exclusion intervals are associated to each switch output port and represent the nodes that are unreachable from this port after a fault. We propose a methodology to identify the links where the exclusion intervals must be updated after a fault, the values to write on them, and a very efficient mechanism to distribute the required information through the network without stopping the system activity. Our methodology can tolerate a high number of network failures with a low degradation in performance. Moreover, it can achieve zero packet losing during the updating period.