The output of the decorrelator matched to the user of interest does not have the signal of interfering users. Does the number of interfering users have an effect on the bit-error-probability (BEP) of the decorrelator? From previous research, we cannot know the impact of the number of users on the BEP. We give the relation between the BEP and the number of users and its mathematical proof is also presented. From the process of the mathematical proof, we can explain some phenomena. Based on the relation of the decorrelator to the number of users, we propose a wavelet-based reduced-dimension approach for joint space-time multiuser detection to reduce its computation load. Compared with the full dimension decorrelator, although the dimension of our algorithm is reduced, the performance does not decrease under the condition of low input SNR and large number of users. Simulations confirm our results.