In this paper, we propose a new transmit beamforming technique for multiple-input-multiple-output (MIMO) systems to improve the link level performance. We present a method for orthogonalization of two complex-valued vectors by introducing a variation of the Jacobi rotations. We will show that based on the proposed rotation transformations, the orthogonality can be established among different complex-valued column vectors in the channel response matrix. Utilizing the orthogonality, we can achieve the channel gain comparable to the maximum singular value of the channel matrix. Simulation results demonstrate that the proposed beamforming scheme achieves the near-optimum performance with much reduced complexity and feedback overhead. Especially, for the two transmit antenna case, we show that the proposed beamforming scheme provides the optimal beamforming vector for MIMO systems.