Security and privacy vulnerabilities in RFID authentication protocols may affect RFID users by revealing their identification information especially in Healthcare systems. Previous researches in RFID authentication protocols have mainly focused on authenticating the real tag's secret key and identifier, which may help attackers directly obtain these important values. Therefore, in this paper, we present new initialization (IA) and termination (TA) stages of an RFID authentication protocol that improves the RFID security and privacy by authenticating the tag and the server without using the real tag's values (secret key and identifier). If the tag and the server pass the initial stage of authentication (IA), Any authentication protocol can be applied to send and receive the real identification values between them.