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We propose a new non-iterative coordinated beamforming scheme to obtain full multiplexing gain in 2-user MIMO systems. In order to find the beamforming and combining matrices, we solve a generalized eigenvector problem and describe how to find generalized eigenvectors according to the Gaussian broadcast channels. Selected simulation results show that the proposed method yields the same sum-rate performance as the iterative coordinated beamforming method, while maintaining lower complexity by non-iterative computation of the beamforming and combining matrices. We also show that the proposed method can easily exploit selective gain by choosing the best combination of generalized eigenvectors.