From 1820 4 times 4 binary matrices, 253 binary preprocessing matrices are designed for double space-time transmit diversity (DSTTD) systems with two 2 times 2 space-time block code (STBC) encoders. Among them, six matrices yielding the highest average minimum-post-processing SNR are proposed from numerical experimentation under uncorrelated channel conditions. The proposed preprocessing performs a superposition of the first and second (second and first) STBC symbols and a selection of two transmit antennas. Simulation results show that the proposed method provides 1.7 dB (1.8 dB) SNR improvement in uncorrelated (correlated) channel environment at 10-3 bit error rate over the conventional antenna shuffling method.