Ind-privacy and unp-privacy, later refined to unp*-privacy, are two different classes of privacy models for RFID authentication protocols. These models have captured the major anonymity and untraceability related attacks regarding RFID authentication protocols with privacy, and existing work indicates that unp*-privacy seems to be a stronger notion when compared with ind-privacy. In this paper, we continue studying the RFID privacy models, and there are two folds regarding our results. First of all, we describe a new traceability attack and show that schemes proven secure in unp*-privacy may not be secure against this new and practical type of traceability attacks. We then propose a new unpredictability-based privacy model to capture this new type of attacks. Secondly, we show that this new model, where we called it the unpτ -privacy, is stronger than both unp*-privacy and ind-privacy. © 2013 Springer-Verlag.