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We propose a new relaying scheme referred to as space full-duplex max-max relay selection (SFD-MMRS), which uses relay selection and half-duplex (HD) relays with buffers to mimic full-duplex (FD) relaying. SFD-MMRS allows the selection of different relays for reception and transmission, which, in turn, enables the relays selected for reception and transmission to simultaneously receive and transmit. With SFD-MMRS, the prelog factor 1/2 is removed from the capacity expression, and better performance in terms of both throughput and outage probability is achieved. We provide a comprehensive analysis of the capacity and outage probability of the proposed scheme for a decode-and-forward (DF) protocol in Rayleigh fading. This analysis reveals that the proposed scheme provides better performance, compared with HD MMRS and HD best relay selection (BRS). Moreover, our simulation results show that the capacity of the proposed scheme with HD relays exceeds twice the capacity of BRS with HD relays for any number of relays. Furthermore, the proposed scheme provides full diversity and large signal-to-noise ratio (SNR) gains, compared with competing schemes in the literature.