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Mobile ad hoc networks (MANETs) are characterized by wireless connectivity through multi-hops, frequently changing network topology among wireless mobile devices. These characteristics require routing algorithms to be dynamic and adaptive to constantly changing environments. In this paper, we describe a new routing algorithm which is based on the cumulative relative stability among neighbor mobile nodes. This NSR (neighbor stability routing) algorithm selects the most historically and accumulatively stable mobile nodes to form a path between the source node and destination node. The relative stability is then propagated from the collective data by all the nodes along a path. The cumulative collective data, or stability factor, reflects the historical neighborhood stability among neighbors. When a node or segment on the path is down, NSR will dynamically find an alternative most stable path. In simulation, our NSR algorithm outperforms some major ad hoc routing protocols such as AODV and DSR in packet delivery ratio and number of paths rerouted. NSR also handles some issues such as group node mobility and temporary node unavailability well.