Transmit diversity in the presence of channel feedback at the transmitter is analyzed in this paper. We first consider perfect channel feedback and summarize the beamforming solution which minimizes the codeword error probability. We note that the error probability minimizing scheme is different from the mutual information maximizing scheme. We then present a scheme with partial channel feedback in the form of relative phases of channel vectors. This scheme achieves performance comparable to the beamforming with much less information about the channel, which in turn requires less resources for feedback. The new scheme presented in this paper is a generalization of a well known scheme for two transmit and one receive antenna, using the phase difference of the channel coefficients.