In this paper we propose a sub-optimal relay selection scheme over a multiple relay network where the relay node is selected if its link quality is above a certain threshold which is set to satisfy the required performance and the selected link is maintained unless its link quality does not fall below the threshold. From our derived statistics of the received output signal-to-noise ratio (SNR), we derive the end-to-end system performance in terms of the outage probability. In addition, we apply our proposed algorithm to the selection decode-and-forward protocol, and analyze its outage performances. We show from our numerical example that our proposed algorithm can provide adequate performance by setting the moderate threshold while its complexity is much lower than the one of an optimal relay selection scheme.