In recent years, radio frequency identification (RFID) technology has been applied in various fields to identify objects efficiently. Anti-collision protocols are important for RFID tag identifications because it can overcome the problem of unsuccessful identification caused by simultaneous transmission of IDs from multiple tags. Considering that identification is usually performed multiple times, the latest anti-collision approach uses the previous identification results for later identifications, and can identify two tags per unit time. Existing anti-collision protocols ignore bit information, causing low performance problems. In this study, we propose a new approach called multiple resolution bit tracking protocol (MRB) to improve this performance further. This approach dynamically computes a tag set that can be unambiguously identified irrespective of any missing sub-set. The tags in the tag set are requested to transmit their IDs in the same time slot and terminate their identifications after proper processing. We perform extensive simulations to validate the performance of our proposed approach. The results show that MRB can achieve 3.7 tags per unit time, which is 1.85 times the number achieved using the existing approaches.