Recently, a quasi-orthogonal space-time block code (QSTBC) capable of approaching the maximum outage mutual information of a MIMO system for the case of four transmit and one receive antennas was proposed. Based on the generalization of these QSTBC to 2(n) transmit antennas and arbitrary number of receive antennas, we analyze the impact of antenna selection (AS) by choosing one out of n(R) receive antennas based on different selection criteria on both the outage probability and the bit error rate. Furthermore, we derive a lower bound for the fraction of outage probability achieved with QSTBC combined with AS. Simulation results show, that even the ZF-detector with AS outperforms the ML-detector without AS by using only one extra antenna, thereby dramatically reducing the computational complexity of the receiver.