In this paper, we propose a low complexity linear multiuser beamforming system for the multiple-input multipleoutput (MIMO) broadcast channel. We consider the specific case of transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which an iterative algorithm is required to design the beamformers, we first provide a low complexity non-iterative solution via the generalized eigenvector decomposition to jointly optimize transmit beamforming and receive combining vectors. The proposed beamforming technique works for two or more transmit and receive antennas where perfect channel state information is available at the transmitter. To enable practical implementation, a new non-uniform limited feedback algorithm is also proposed that exploits the structure of the algorithm to avoid full channel quantization especially for two transmit antenna systems. The feedback overhead is independent of the number of receive antennas. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.