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We propose a multihop cooperative routing (MCR) algorithm that extends the lengths of the x axis projections of the hop distances and finds the multihop route that minimizes the number of hops in spectrum sharing networks. The cognitive relay and the cognitive receiver of each hop except the last one are selected by the following procedures. First, the cognitive node that is nearest away from the cognitive sender is selected as the cognitive relay, and let the cognitive destination (CD) be the cognitive receiver. Then, if the participation of the selected cognitive relay can not satisfy the QoS requirement of the cognitive transmission, among the cognitive receiver candidates that satisfy the QoS requirement of the cognitive transmission, the one whose x coordinate has the largest difference from that of the cognitive relay is selected as the cognitive receiver. At the last hop, if the cognitive relay is available, the cooperative transmission is performed. Otherwise, the direct transmission is performed. Simulation results show that the MCR reduces the average number of hops compared to the FNR and outperforms the FNR in terms of the average end-to-end reliability, the average end-to-end throughput, and the average required transmission power.