While multiple-input multiple-output (MIMO) system gives many advantages to wireless communication, the complexity of multiple RF chains gives a burden to the system. Antenna selection is introduced as a technique to reduce the burden. On the transmit antenna selection scheme, the exhaustive search for optimal antenna set quickly becomes impractical as adopting more antennas. To reduce complexity for searching, we propose an efficient transmit antenna selection method. We first make a threshold for optimal antenna set by using Poincare separation theorem. Instead of exhaustive search, we select a transmit antenna subset that exceeds the threshold. On the exponentially correlated channel of array antennas, we give an order to search for reducing complexity further. We search from the most remotely located antenna subset which in generally less correlated to the closely located antennas which is more correlated. Finally, we show the BER performance and tradeoff relation between performance and complexity by Monte-Carlo simulations.