This letter presents a criterion for selecting a transmit antenna subset when ZF detectors followed by Rake combiners are employed for spatial multiplexing (SM) ultra-wideband (UWB) multiple input multiple output (MIMO) systems. The presented criterion is based on the largest minimum post-processing signal to interference plus noise ratio of the multiplexed streams, which is obtained on the basis of QR decomposition. Simulation results show that the proposed antenna selection algorithm considerably improves the BER performance of the SM UWB MIMO systems when the number of multipath diversity branches is not so large and thus offers diversity advantages on a log-normal multipath fading channel.