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In this paper, the impact of diversity order on symbol error rate (SER) performance is investigated for the cooperative amplify-and-forward (AF) multiple-input-and-multiple-output (MIMO) relaying system under the average power scaling (APS) constraints. Furthermore, the optimal power allocation (OPA) scheme is proposed based on the criterion of maximizing signal-to-noise-ratio (SNR). Through the SER analysis and numerical results, it can be shown that the diversity order in AF MIMO relaying system under APS is MT (the number of transmitting antennas) when uniform power allocation (UPA) is adopted. Given MR receiving antennas at the relay nodes, the proposed novel OPA scheme can not only reduce the SER but also improve the diversity order efficiently up to MR even when MT = 1.