Antenna selection is a simple but effective method to exploit the transmit diversity in multiple-input multiple-output (MIMO) wireless communications. For maximum-likelihood (ML) detectors, the criterion for the selection is to maximize the free distance of the MIMO system. Since the optimum selection is difficult to conduct, a lower bound of the free distance is typically used as the selection criterion instead. The singular-value-decomposition (SVD) based selection criterion is well known in the literature. In this paper, we propose a QR decomposition (QRD) based selection criterion for antenna selection with the ML detector. Using some matrix properties, we theoretically prove that the lower bound achieved with the QRD-based criterion is tighter than that with the SVD-based criterion. We also propose another QRD-based criterion that can further tighten the lower bound. The proposed algorithms can be directly applied to the receive, and joint transmit/receive antenna selection schemes. Simulations show that the performance of the proposed selection criteria can significantly outperform the SVD-based selection criterion.