Routes in an ad hoc network may fail frequently because of node mobility. Stability therefore can be an important element in the design of routing protocols. The node escape probability is introduced to estimate the lifetime and stability of link between neighboring nodes and the escape probability based routing (EPBR) scheme to discover stable routes is proposed. Simulation results show that the EPBR can discover stable routes to reduce the number of route rediscovery, and is applicable for the situation that has highly dynamic network topology with broad area of communication.