An optimal power allocation (OPA) method with mean channel gains is proposed for a multinode amplify-and-forward cooperative communication system. By making use of M-PSK modulation, a closed-form symbol-error-rate (SER) formulation and corresponding upper bound are first derived. Subsequently the OPA method is utilized to minimize the SER. Comparison of the SER of the proposed OPA method with that of the equal power allocation (EPA) method, shows that the SER of both methods, which is approximately optimal performance, is almost the same when relays are near the source. OPA outperforms the EPA when the relays are near the middle between the source and destination or near the destination. The proposed OPA method depends only on the ratio of mean channel gains of the source-to-relay to those of the relay-to-destination. Extensive simulations are performed to validate the theoretical results. By making use of M-PSK modulation, a closed-form symbol-error-rate (SER) formulation and corresponding to The above OPA method is utilized to minimize the SER. Comparison of the SER of the proposed OPA method with that of the equal power allocation (EPA) method, shows that the SER of both methods, which is approximately optimal The proposed OPA method depends only on the ratio of mean channel gains of the source -to-relay to those of the relay-to-destination. Extensive simulations are performed to validate the theoretical results.