2DPalmHash Code (2DPHC), which is constructed based on Gabor filter, is a cancelable palmprint coding scheme for secure palmprint verification. In this scheme, multiple-translated matchings between two 2DPHCs are performed to remedy the vertical and horizontal dislocation problems of Gabor feature matrix. According to the analysis, vertical translation matching fixes the vertical dislocation, but the horizontal translation matching does not work out horizontal dislocation. Therefore, the computation of multiple-translated matching of 2DPHC can be reduced by discarding the horizontal translation matching. The matching reduction not only reduces the computational complexity of matching, but also improves the verification performance and enhances the changeability capacity of 2DPHC as a cancelable scheme.