We propose transmit antenna selection with maximal-ratio combining (TAS/MRC) for use in multiple-input multiple-output (MIMO) multiuser relay networks (MRN). The network under consideration is equipped with N-S, N-R, and N-D antennas at the source, the relay, and each of the K destinations, respectively. For this network, the destination with the highest instantaneous end-to-end signal-to-noise ratio (SNR) is scheduled for transmission. In each hop, a single transmit antenna that maximizes the post-processing SNR is selected, while all the receive antennas are MRC combined. We first derive new closed-form expressions for the outage probability and the symbol error rate (SER) for amplify-and-forward (AaF) relaying. Next, we present compact and easy-to-compute expressions for the diversity order and the array gain to provide practical insights into the network behavior. We highlight the fact that our proposed scheme attains the maximum diversity order of N-R x min{N-S, NDK}.