Block diagonalization (BD) and coordinated beamforming (CBF) are two major signal processing schemes to achieve the sum rate close to the sum capacity of a multiuser multiple-input multiple-output (MU-MIMO) downlink. However, they do not achieve the full spatial multiplexing gain except under a special antenna configuration. In this paper, therefore, we propose a new linear precoding algorithm for achieving the full spatial multiplexing gain in a general antenna configuration. To obtain the full spatial multiplexing gain, the proposed algorithm divides the users into the two groups in terms of the number of data streams transmitted. In addition, to maximize the sum rate, we choose the member of each groups by comparing the eigenvalues of each effective channel. Simulation results confirm that the proposed scheme performs close to the sum capacity and achieves the full multiplexing gain.