Fat-tree is one of the most important topologies of interconnection networks. Several routing algorithms have been proposed for fat-tree topology. Among them, the OSRM routing algorithm is proved to be an optimal routing algorithm. However, all these algorithms ignore the ease of diagnosis of linkfault. Therefore, based on OSRM, a novel routing algorithm, named BT-OSRM, is proposed. In the BT-OSRM algorithm, the less-equal-great relationship between any pairs of processing nodes is defined, and hence the routing path is chosen from the OSRM routing path and its back-track routing path based on the defined relationship. Further, the BT-OSRM2 and BT-OSRM3 algorithms are described in detail for the commonly used two stages and three stages fattree topologies respectively. Theoretical analysis shows that the BTOSRM algorithm not only is as deadlockfree, loadbalanced and optimal as the OSRM algorithm, but also can guarantee the back-track feature for routing between any two endnodes, thus facilitating the diagnosis of linkfault in interconnection networks.