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In this paper, we study the performance of a downlink hybrid satellite-terrestrial cooperative network. The decode-and-forward scheme is used and a selection of the best relay terminal is implemented. In this proposed system, a two time-slot scenario is considered. The first time slot is used by the satellite for broadcasting the information to the terrestrial relays and the destination. In the second time slot, only the best relay which provides the maximal received signal-to-noise (SNR) ratio at the destination is selected for forwarding the information. Then, both signals are combined using the maximum ratio combining (MRC) technique. The analytical expression of the outage probability is evaluated and is then verified with the simulation. The results show that our analytical expression matched well to the simulation results at the high SNR regime.