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Multiple antenna wireless communication systems have recently attracted significant attention due to their higher capacity and better immunity to fading as compared to systems that employ a single-sensor transceiver. Increasing the number of transmit and receive antennas enables to improve system performance at the price of higher hardware costs and computational burden. For systems with a large number of antennas, there is a strong motivation to develop techniques with reduced hardware and computational costs. An efficient approach to achieve this goal is the optimal antenna subset selection. In this paper, we propose a fast antenna selection algorithm for wireless multiple-input multiple-output (MIMO) systems. Our algorithm achieves almost the same outage capacity as the optimal selection technique while having lower computational complexity than the existing nearly optimal antenna selection methods. The optimality of the proposed technique is established in several important specific cases. A QR decomposition-based interpretation of our algorithm is provided that sheds a new light on the optimal antenna selection problem.