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This paper introduces a new beamforming method for a two-way relay system, where two single-antenna terminals exchange messages via a multi-antenna amplify-and-forward (AF) relay operating in the half-duplex mode. The optimization problem under consideration is to design a relay beamforming matrix that maximizes the achievable weighted sum rate under the relay power constraint, given the channel state information. This problem is non-convex, and iterative optimization algorithms and suboptimal beamformers with reduced complexity have been developed in previous works. In this paper, we develop an alternative suboptimal scheme by converting the original non-convex optimization into convex optimization. This conversion is made possible through some changes of variables and an additional condition. The simulation results demonstrate that the proposed method performs almost as well as the optimal scheme and can yield larger achievable rates than conventional suboptimal beamformers.