Recently linear processing strategies have been developed to approach the optimum performance of dirty paper coding with low complexity in multiuser multiple-input multiple-output (MIMO) downlink systems. In this paper, we propose a new linear coordinated beamforming algorithm which is applicable to the systems with an arbitrary number of antennas and users. Unlike other conventional methods, our scheme exploits the orthogonalized effective channels to yield the transmit beamforming and receive combining vectors. As the proposed scheme generates a solution in a non-iterative fashion, it is more feasible than other iterative schemes. Simulation results show that the performance of our proposed scheme is very close to the conventional iterative scheme with significantly reduced complexity. For a system equipped with four transmit and four receive antennas with two users, the proposed scheme exhibits the bit error rate (BER) comparable to the conventional scheme with a complexity reduction of 79%.