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We present a new transmit scheme based on Alamouti codes for four transmit antenna systems with phase feedback. We propose a pre-processor for combining two Alamouti codes in terms of Frobenius norm maximization. For the proposed scheme, full diversity is achieved by the combining effect at the pre-processor. Also the phase feedback is utilized to increase an array gain. Simulation results show that the performance degradation due to the quantized feedback in the proposed scheme is small, and thus the proposed scheme exhibits a performance gain over existing closed-loop schemes with the same number of feedback bits.