For a single-relay amplify-and-forward (AF) non-cooperative system, an optimal power proportion between source and relay is considered. Aiming to minimize end-to-end bit error rate (BER) and maximize attainable rate, both large-scale path loss and small-scale Rayleigh fading are taken into account. A closed form expression to allocate power in optimal proportion at source is obtained. Simulation results show that the proposed scheme to distribute power can minimize BER under any channel conditions.