Untraceable RFID authentication protocols for EPC compliant tags Radio Frequency Identification (RFID) technology is recently found in the most authentication and identification applications. In the last decade, different RFID authentication protocols have been proposed. In 2007, Chien and Chen proposed an improved authentication protocol for RFID systems that is one of the most challenging protocols in the last few years. In 2012, two different protocols have been proposed based on Chien and Chen’s protocol by Zhang et al. and Huang-Jiang. In this paper, the privacy of Zhang et al.’s and Huang-Jiang protocols that both are under Electronic Product Code Class1 Generation 2 (EPC C1 G2) standard is analyzed. It is shown that the privacy of both protocols has some weaknesses and both protocols are not secure against different traceability attacks. Then, in order to enhance the privacy of the analyzed protocols, two improved versions of them are proposed. The analyses show that the improved protocols omit all existing weaknesses of Zhang et al.’s and Huang-Jiang protocols and can provide privacy for RFID users.