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In cognitive networks, the existing RASR routing algorithm does not consider channel usage ratio of the PU and results in an unstable path problem. To address these issues, a new Routing Selection Algorithm in Cognitive mesh networks (RSAC) is proposed in this paper. RSAC is designed by piggybacking the information of link stability factor which is the sum of the channel usage ratio of secondary users and choosing routes based on it. It enhances the route stability, improving the success ratio of data packets transmission, reducing the average end-to-end delay. Theoretical analysis and simulation results show that RSAC outperforms the RASR routing algorithm in terms of the success ratio of data packets transmission, the average end-to-end delay.