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In this paper, we propose a non-redundant preceding-assisted blind channel estimation scheme for the improper orthogonal frequency-division multiplexing (OFDM) systems. In the proposed scheme, a modified cross-correlation matrix of the augmented received signal is obtained by dividing the cross- correlation matrix of the even-indexed and odd-indexed OFDM received signal by the precoding matrix element-wise. The channel coefficient vector is estimated as a principal eigenvector of the modified cross-correlation matrix, and it is obtained by the computationally simple power method without the need of the complicate eigenvalue decomposition. Simulation results show that the channel estimation and bit error rate (BER) performance of the proposed scheme is superior to that of the conventional preceding-assisted blind channel estimation scheme.