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Cooperative transmission is an efficient solution to improve the performance of wireless communications over fading channels without the need for physical co-located antenna arrays. Current cooperative transmission schemes for two users can only achieve maximum diversity order of 2. In this paper, we propose a novel cooperative transmission scheme with amplify-and-forward relay which can obtain the diversity order of 3. Its closed-form BER expression is also derived and confirmed by Monte-Carlo simulations. A variety of simulated and numerical results under flat Rayleigh fading channel plus AWGN (Additive White Gaussian Noise) shows that the proposed scheme saves a significant amount of consumed power compared to non-cooperation counterpart subject to the same BER performance and bandwidth efficiency.