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In this correspondence, we propose an efficient low-complexity relay-destination selection scheme for multiuser multirelay downlink cooperative networks comprised of one source node (base station), L destination nodes (mobile terminals), and N relay nodes. Our scheme first selects the best destination node based on the channel quality of the direct links and then selects the best relay that yields the best path from the source to the selected destination. Assuming both decode-and-forward (DF) and amplify-and-forward (AF) relaying strategies, the outage performance of the considered system is studied. Closed-form expressions for the outage probability are derived and validated by means of Monte Carlo simulations. For the AF case, both variable-gain relaying and fixed-gain relaying are examined. In our analysis, the source node may be equipped with either a single antenna or M multiple antennas. An asymptotic analysis is carried out, and it reveals that, regardless of the relaying strategy employed, the diversity order reduces to L + N for the single-antenna source case, whereas it is equal to ML + N for the multiple-antenna source case. The effects of the number of relay and destination nodes on the system performance and its influence on the best relay position are examined. In addition, a tradeoff concerning the system performance and spectral efficiency is observed when multiple antennas are employed at the base station. More specifically, on one hand, by increasing the number of antennas, the outage performance is increased. On the other hand, the system loses in terms of spectral efficiency.