Multi-modal biometrics enjoy more merits than their single-modal counterparts in terms of accuracy performance and security. The fusion of hand-based biometrics such as palmprint and palmvein is straightforward since they can be acquired simultaneously with a customized image acquisition device. Conjugate 2DPalmHash Code (CTDPHC), which is constructed by 2DPalmHash Codes (2DPHCs) of palmprint and palmvein, is proposed as a cancelable multi-modal biometric. To determine the proper fusion strategy of 2DPHCs of palmprint and palmvein, different fusion rules at score level are compared and discussed. The transposition orientation ranges of 2DPHCs are also finetuned to improve the accuracy performance. Compared with 2DPHC, CTDPHC enjoys higher verification accuracy and stronger anti-counterfeit ability, while trades neither computational complexity nor storage cost.