Employing relays for communication between a source and a destination increases diversity, owing to the additional paths for the signals to traverse and improves coverage once the direct link between the source and the destination becomes too weak. Relay Selection (RS) wherein only a single selected relay is put into the active mode includes advantages such as reducing loss in spectral efficiency, lesser degree of co-ordination & also provides superior overall performance. Design of relay selection is done under an imperfect (uncertain) knowledge of long-term (instantaneous) Channel State Information (CSI) at relay nodes. Optimization scheme is done by Minimax algorithm to arrive at a robust RS approach that promises the best guarantee on the worst-case end-to-end signal-to-noise (SNR) ratio and also in terms of average Bit Error Rate (BER) performance. In the Minimax algorithm, the selected relay performed based on the CSI uncertainty. This alone not provided perfect relay selection, which will be improved by the power split between the source and selected relay. The optimal minimax robust relay selection for the maximization of destination SNR, under a total power constraint is achieved by selecting the best relay.