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This paper proposes a novel sub-optimal transmit antenna selection (TAS) strategy for non-regenerative half-duplex MIMO relay channel. While antenna selection is a sub-optimal form of beamforming, it still enjoys the advantage of tractable optimization and low feedback overhead. The diversity order of this proposed strategy is derived to prove that it can achieve the full diversity order as the optimal strategy with only a small performance loss. Furthermore, it is shown that our scheme lead to a reduction of complexity in terms of time slots for SNR estimation when the number of the transmit antennas are more than two. Monte Carlo simulation results of outage probability are presented to demonstrate its advantage over the other two conventional TAS schemes.