Thanks to their flexibility and their simple installation, Wireless Mesh Networks (WMNs) allow a low cost deployment of a network infrastructure. They can be used to extend the wired network coverage allowing connectivity anytime and anywhere. Network stability is a key performance metric in supporting real time communication over the network. Because of high bandwidth demand and dynamic traffic variation, several paths in WMNs are expected to be unstable. High levels of network instability can lead to interferences, packet losses and high delays. In this paper, we address the stability problem of WMNs; instability in these networks is caused mainly by link quality fluctuations and frequent route flapping. Indeed, most routing protocols try to optimize a routing metric locally or globally without considering network stability. First, we present the key factors that may cause network instability; then, we propose a new technique, called Local Node Stability-based Routing (LNS), using the entropy function (known as a measure of the uncertainty and the disorder in a system) to define a node stability. Simulation results show that the stability can be improved in WMNs using LNS compared to other routing schemes namely RLBDR, MIC and ETX.