We study a type of cooperative relay, which is among secondary users. In this type of cooperative relay, some secondary users may have more spectra than needed; therefore, they can use their spare spectrum to relay traffic for other secondary users. While this type of cooperative relay has been studied extensively, a crucial problem in this type of cooperative relay lies in the (lack of) incentives for the potential relay nodes. To address this problem, we propose that relay nodes should receive payments for their relay services so that they have incentives to provide such services. Specifically, we design a Market for Incentive-compatible COoperative Relay (MICOR). MICOR allows each potential relay node to submit a valuation function, which describes how much payment its relay service is worth. MICOR guarantees that, under a precondition called No Monopoly, it is a Dominant Strategy Equilibrium for all potential relay nodes to submit their true valuation functions. To establish this precondition, we also design an algorithm for channel assignment that achieves the optimal monopoly reduction with a very high probability. Results of extensive evaluations demonstrate that MICOR provides strong incentives to potential relay nodes, effectively reduces monopoly, and has good efficiency.