We propose a new cooperation protocol for the fading multiple-access channel called space-division relay (SDR). It is similar to the protocol of Laneman, Tse and Wornell (LTW) [1], except that the relays use space-division instead of time-division multiplexing. The result is a nonorthogonal cooperation protocol with a higher rate that nevertheless achieves the full diversity of the two-user Rayleigh-fading cooperative multiple-access channel, a result that. is proven in this paper. We examine the SDR protocol with two types of relays: the amplify-and-forward (AF) relay and the amplify/decode-and-forward (ADF) relay. We derive the outage probability of the proposed scheme with AF relays. We present numerical results for the two-user channel at 1 bps/Hz which show that SDR-ADF outperforms all previously reported cooperative schemes. In particular, in terms of the SNR required to achieve a 10(-3) outage probability, the SDR-AF protocol outperforms the LTW-AF protocol by 1.9 dB, while the SDR-ADF protocol outperforms another nonorthogonal protocol called NAF [4] by 1 dB, failing only 2.3 dB short of the ideal cooperation bound.