Digital fingerprinting of multimedia data involves embedding information in the content signal and offers the traceability of illegal users who distribute unauthorized copies. One potential threat to fingerprinting system is collusion, whereby a group of users combines their individual copies in an attempt to remove the underlying fingerprints. Hayashi et. al have proposed hierarchical fingerprinting scheme using the CDMA technique which designed a fingerprint signal by a combination of quasi-orthogonal sequences to increase the allowable number of users. In this paper, we formalize the model of collusion from the viewpoint of a communication channel, and propose a removal operation considering the interference among fingerprints. We also explore the characteristic of the proposed detector and the effects of the removal operation on a detection sequence. By introducing two kinds of thresholds for the determination of the presence of fingerprints, the performance of the proposed detector is enhanced effectively.