Recently it is shown that the maximum MIMO beamforming gain can be achieved using only one RF (radio frequency) chain. This is done by implementing the beamformer using Two analog pHase shIfters for each Coefficient (THIC). In this paper we analyze the quantization error of the beamforming coefficients (weights) when the phase shifters used in THIC are of finite resolution. An alternative THIC structure is proposed. The new structure, having the same beamforming gain when the phases can take on continuum values, behaves differently upon quantization. It can achieve a smaller quantization error through proper allocation of quantization bits between the two phase shifters. Simulations are given to demonstrate that a performance very close to the full MIMO beamforming gain can be achieved using phase shifters of low resolution.