In the IEEE 802.16j standard, the relay station has been introduced to increase the coverage and the throughput of WiMAX networks. The placement of the relay station plays a critical role in the system performance and therefore draws tremendous attention from the research community. In this paper, we study the relay station placement problem in the WiMAX network, with the cooperative communication as the relaying strategy. In particular, given a base station and a set of subscriber stations, we determine the location of a relay station, and the set of subscriber stations using the relay station. The objective is to minimize the maximum transmission power among all the subscriber stations while satisfying the data rate requirements of the subscriber stations. We develop a near-optimal algorithm to solve this problem and prove that the maximum transmission power computed by our algorithm is at most P opt + ε, where P opt is the maximum transmission power in the optimal solution and ε > 0 is an arbitrary constant. The experiments show that we can dramatically reduce the maximum transmission power by deploying the relay station according to our algorithm.