In ad-hoc on-demand routing algorithm, when a route is broken a relay node must perform error transaction and the source node must do rerouting to discover an alternate route. It is important to construct a stable route when route discovery occurs. In this paper, we use relative speeds among nodes as a measure of node mobility. Our routing algorithm chooses nodes of lower relative speed as relay nodes. As a result of our simulation, when there is one session in the network, our proposing algorithm can reduce the number of route breaks: about 3 times smaller than DSR. And our proposing algorithm can deliver more packets than DSR: 18% higher rate. However, in the congested traffic situation our algorithm should be improved.