RFID tag search system can be used to find a particular tag among numerous tags. In 2011, Chun et al. proposed an RFID tag search protocol preserving privacy of mobile reader holders. Chun et al. claimed that their proposed protocol can withstand five attacks to be considered in serverless search protocols, such as tracking, cloning, eavesdropping, physical, and Denial of Service (DoS) attacks. However, this paper points out that the Chun et al.’s protocol still can be vulnerable to the DoS attack.