A precoder is designed for orthogonal space–time block codes (OSTBCs) for arbitrarily correlated Ricean multiple-input multiple-output (MIMO) channels. Unlike previous literature, our precoder is the first to be designed to minimize the exact symbol error rate (SER) as a function of both a) the joint transmit–receive channel correlation coefficients and b) the MIMO Rice component, which are fed back to the transmitter. It is important to note that the covariance may or may not follow the so-called Kronecker structure. Exact SER expressions are given for multilevel PAM, PSK, and QAM signaling. Several properties of the minimum exact precoder are provided. An iterative numerical optimization algorithm is proposed for finding the exact minimum SER precoder under a power constraint.