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A linear precoder is designed to minimize an upper bound of the pairwise error probability (PEP) when using arbitrary space-time block codes (STBC) over correlated Ricean fading channels. The proposed precoder design differs from the previously proposed precoders as follows: 1) Existing precoders are applicable when there exists only transmit correlation and no receive correlations, however, the proposed precoder is applicable to correlated Ricean MIMO channels with an invertible correlation matrix. 2) We minimize the upper bound of the PEP of non-orthogonal STBC for obtaining a precoder over correlated Ricean channels, whereas, one existing precoder minimizes an upper bound of PEP for orthogonal STBC (OSTBC). The proposed precoder outperforms two existing precoders for non-orthogonal STBC especially for highly correlated channels.