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This paper presents a closed-form blind channel estimation scheme for orthogonal space-time block codes in multiple-input single-output (MISO) systems, with specific focus on Alamouti's code for two transmit antennas. The channel matrix is estimated from the eigenvalue decomposition of the fourth-order cumulant matrix of the received signal. Unlike previous blind estimation schemes for MISO systems, the proposed algorithm is tested with block and slowly fading channels. The proposed scheme performs very well in both cases. A single pilot tuple is required to correctly assign the estimated to the actual channels and to resolve the sign ambiguity common to all blind estimators. It is shown that this scheme outperforms the only other available blind channel estimation scheme for this scenario. To achieve good performance in terms of bit error rate, 100-300 sample points are sufficient to provide accurate channel estimates. The main disadvantage of the proposed scheme is the complexity associated with the estimation of fourth-order cumulants. This complexity is reduced by exploiting the symmetry inherent in the cumulant matrix.