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In this paper, we present a low-complexity method to generate a transmit beamforming vector for multiple-input-multiple-output (MIMO) systems. We begin by introducing new definitions regarding orthogonality between two complex valued vectors and then present new expressions of complex rotation matrices for the complex vector orthogonalization. The rotation matrices are utilized to derive the weight vector for the maximum-norm combining (MNC) process of two complex vectors, which provides a constructive basis for a new beamforming method. The proposed transmit beamforming method uses successive column combining of MIMO channel matrices based on MNC, and as a result, an approximate solution to the optimum beamforming vector is obtained. The proposed method offers a good tradeoff between complexity and performance. Simulation results demonstrate that the proposed beamforming method achieves the near-optimal performance with much reduced computational complexity, compared to the optimal beamforming scheme using singular-value decomposition (SVD) of the channel matrix.