Differential orthogonal space‐time block codes (DOSTBC) sent over correlated Rayleigh fading channels are considered in this paper. Approximate expressions for the symbol error rate (SER) are derived for DOSTBC with M‐PSK, M‐PAM, and M‐QAM constellations assuming arbitrary correlation between the transmit and receive antennas. A full memoryless precoder is designed to improve the performance of the DOSTBC over correlated Rayleigh MIMO channels. The proposed precoder design differs from the previous work: (1) our precoder design considers arbitrary correlation in the channels, whereas the previously proposed precoder design considers only transmit correlations in the Kronecker correlation model; (2) the proposed precoder is based on minimizing proposed SER, whereas the previously proposed precoder is based on minimizing the Chernoff bound of approximate SER; (3) we propose precoder design for DOSTBC with M‐PSK, M‐PAM, and M‐QAM constellations, whereas the previously proposed precoder works for DOSTBC with M‐PSK only. Additionally, the proposed precoded DOSTBC outperforms the conventional eigenbeamforming‐based precoded DOSTBC for the Kronecker model with only transmit correlation.