Quantized feedback in multiple antenna systems has the potential to increase throughput and/or reduce probability of outage. However, current beamforming code-book designs lead to large implementation complexity of the channel quantizer. We propose a vector mapping scheme to construct beamforming codebooks from existing codebooks. We show that beamforming codebooks constructed via the proposed vector mapping have a structure that allows an efficient immplementation of the channel quantizer. We show that the proposed vector mapping can also be used to simplify the implementation of the chanel quantizer in a WiMAX compliant system, where the codebooks have already been defined. Simulation results validate the proposed codebook construction method.