This paper proposes a novel and efficient iterative antenna selection algorithm based on an SNR selection criterion for a multi-input-multi-output (MIMO) system employing orthogonal space time block codes (OSTBCs), specifically Alamouti codes. The proposed algorithm addresses the open problem of finding a suboptimal set of transmit and receive antennas that performs close to the globally optimum configuration selection solution at significantly reduced complexity. Also, the paper is proposing a method to incrementally update the selected set of antennas, so as to enable even greater complexity reduction, and in particular, for the case of channels with temporal or time correlation. To date, antenna selection has not been assessed under temporal correlation. Simulation results show promising average bit error rate (ABER) performance gain after only a small number of iterations.