The simple and cheap passive RFID tag systems have recently been used for efficient localization of indoor mobile robots, where each RFID tag stores its own absolute position and the mobile robot carrying an RFID reader scans the RFID tags to localize itself. The available localization schemes using passive RFID systems do not consider the scanning delay which may cause location estimation error especially when the robot moves with a high speed. In this paper, a new Non-Blocking scanning (reading) scheme is proposed to avoid collisions such that the scanning delay and consequently the localization error can be reduced. This scheme avoids collision among tags replies by assigning tags IDs based on the FCA coloring scheme. Theoretical and simulation studies indicate that the new Non-Blocking scheme combined with the new tag arrangement pattern can achieve a good RFID localization performance in terms of both estimation error and scanning delay.