We propose a new closed-loop MIMO (Multiple-Input Multiple-Output) signal processing scheme that combines transmit beamforming and spatial multiplexing in Rayleigh frequency-flat fading channel environment. Diversity gain. achieved by beamforming, and multiplexing gain by spatial multi-IS plexing. The proposed scheme is particularly useful for downlink communication, where the number of transmit antennas at the base station is greater than the number of receive antennas at the mobile. Beamforming weight vectors are computed at the receiver using the estimated channel matrix and are sent to the transmitter. The computation is based on the mutual information maximization criterion which reduces to a symmetric eigenvalue problem. The BER (Bit Error Rate) performance comparisons with other known schemes are also presented for the cases of the AIL (Maximum Likelihood) decoding and the MMSE (Minimum Mean-Squared Error) nulling and ordered-cancellation decoding, through extensive-Monte-Carlo simulation. The simulation results show that the proposed scheme has lower BER than the other schemes.