Optimum antenna sub-set selection in MIMO systems is an attractive cost reducing technique. In this paper we develop an optimal antenna sub-set selection technique to be used in conjunction with space-time block codes over a MIMO link to optimize link error performance over a fading channel. We study the case when antenna sub-set selection is applied either at the transmitter or the receiver. We provide analytical results for substantial improvement in average SNR and outage capacity when antenna sub-set selection is used. Simulation results that verify our analytical prediction are also presented.