We study the optimal transmission strategy of a single-user multiple-input/multiple-output communication system with covariance feedback. We consider the situation with correlated receive and correlated transmit antennas in Rayleigh flat fading. Furthermore, we assume that the receiver has perfect channel state information, while the transmitter knows only the transmit correlation matrix and the receive correlation matrix. We show that transmitting in the direction of the eigenvectors of the transmit correlation matrix is the optimal transmission strategy. In addition to this, the optimal power allocation is studied and a necessary and sufficient condition for optimality of beamforming is derived. All theoretical results are illustrated by numerical simulations.