A method and system for reduced feedback transmit beamforming computes a matrix of channel transfer function coefficients. The matrix of channel transfer function coefficients is compressed by applying a rotation matrix having orthogonal columns to the matrix of channel transfer function coefficients to produce a compressed transfer function matrix having a reduced number of non-zero coefficients. The compressed matrix is fed back to a transmitting unit. Decompression of the transfer function coefficient matrix is not required. This compression does not cause any performance degradation for transmit beamforming. The transmitting unit computes a set of beamsteering coefficients from the compressed matrix and applies the coefficients to signals prior to transmission. The beamformed signals are transmitted to the receiving unit and post-coded to allow the receiving unit to see an effective diagonalized channel.