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This paper introduces a full rate, full diversity orthogonal space-time block code for 4 transmit antennas. The codeword blocks can be viewed as quaternions which are drawn from the icosahedral group and no constellation expansion. We prove the full diversity of the proposed STBC and analysis the performance under the correlated MIMO channel. By utilizing the quaternionic form, we can find the decoding algorithm to reduce the complexity of maximum likelihood (ML) coherent decoding and introduce a non-coherent differential decoding rule.