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In this paper we present a novel extended orthogonal space-time block coding (EO-STBC) scheme for three and four relay nodes to use in asynchronous cooperative relay networks. This approach attains full-rate and full-diversity in that each hop attains unity rate and all four uncorrelated paths are utilized. Robustness against the effects of random delays at the relay nodes is enhanced through the use of a low-rate feedback channel. A new low complexity phase feedback scheme has been proposed which can retain the advantage of the perfect feedback scheme with substantial reduction in the feedback overhead. Orthogonal frequency division multiplexing (OFDM) with cyclic prefix (CP) is used at the source node to combat the timing errors at the relay nodes, which operate in a simple amplify-and-forward (AF) mode. Simulations show that our new scheme outperforms the previous schemes and uses a very simple symbol-wise maximum-likelihood (ML) decoder.