Radio frequency identification (RFID) chips have been widely deployed in large-scale systems such as inventory control and supply chain management. While RFID technology has much advantage, however it may create new problems to privacy. Tag untraceability is a significant concern that needs to be addressed in deploying RFID-based system. In this paper we propose a new construction for untraceable tags. Our construction is the first construction in the symmetric bilinear setting based on a mild assumption. That is our assumption is tautological in the generic group model and is “efficiently falsifiable” in the sense that its problem instances are stated non-interactively and concisely (i.e., independently of the number of adversarial queries and other large quantities).