We propose the Hadamard matrix as a codebook for multiple-input multiple-output (MIMO) beamforming systems, and show that a quantized equal gain transmission (QEGT) scheme using the Hadamard codebook has the same symbol error probability performance as a receiver selection diversity combining scheme operating in independent generalized Rayleigh fading channels. Also, we propose a greedy cophasing scheme for MIMO beamforming systems using quantized feedback. The greedy cophasing scheme provides 3.2 dB power gain over an orthogonal space-time block code when the number of transmit antennas is four, the number of receive antennas is one, and the number of feedback bits is three.