Ubiquitousness of Radio Frequency Identification (RFID) systems with inherent weaknesses has been a cause of concern about their privacy and security. Therefore, secure protocols are essentially necessary for the RFID tags to guarantee privacy and authentication among them and the reader. This paper inspects privacy in the RFID systems. First, we survey four new-found RFID authentication protocols, and then, their weaknesses in formal privacy model are analyzed. Although the authors of the schemes claimed that their protocols completely resist privacy attacks, we formally prove that all of them suffer from the family of traceability attacks. Furthermore, not only are the four improved protocols proposed to prevent the aforementioned attacks, but also we provide formal analysis to guarantee the security and privacy of the proposed enhancements. Copyright © 2012 John Wiley & Sons, Ltd.