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We design an optimal linear precoder for a space-time coded system assuming knowledge of only the transmit antenna fading correlations. Assuming a flat fading channel and a maximum-likelihood receiver, we show that the linear precoder transmits power on the eigenmodes of the transmit antenna correlation matrix. The power allocation on the eigenmodes is a form of waterpouring policy. Simulation results are presented to show performance improvement on a space-time coded system.