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Dual-cast transmission appears naturally in network coding-based two-way relay systems, where the relay terminal needs to send network coded information to both end users simultaneously. In this paper, we investigate the optimal beamforming design for wireless dual-cast channels. Specifically, we present an efficient closed-form solution of the optimal beamforming vectors and their achievable maximal dual-cast rate for both orthogonal and nonorthogonal user channel cases. Comparison with conventional non-network-coding based schemes shows that the proposed design of dual-cast beamforming with network coding can best explore the capacity benefit of multiple antennas at the relay terminal.