Next to the high performance, the essential feature of the multiprocessor systems is their fault-tolerant capability. In this regard, fault-tolerant interconnection networks and especially fault-tolerant routing methods are crucial parts of these systems. Hypercube is a popular interconnection network that is used in many multiprocessors. There are several suggested practices for fault tolerant routing in these systems. In this paper, a neural routing method is introduced which is named as Fault Avoidance Routing (FAR). This method keeps the message as far from the faulty nodes as possible. The proposed method employs the Hopfield neural network. In comparison with other neural routing methods, FAR requires a small number of neurons. The simulation results show that FAR has excellent performance in larger interconnection networks and networks with a high density of faulty nodes.