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This paper proposes a simple orthogonal frequency -division multiplexing (OFDM) transmission scheme for asynchronous cooperative communications over frequency-selective fading channels. In this scheme, the relay nodes only implement very simple operations on their received signals, and no decoding, DFT or IDFT operation is needed. With our proposal, the received signals have the Alamouti code structure on each subcarrier, and thus, it has the fast symbol-wise ML decoding. The analysis and simulation results demonstrate that our simple scheme can achieve order-two spatial diversity gain for amplify-and-forward based cooperative communications over frequency-selective fading channels in the presence of asynchronization between relay nodes.