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Radio frequency identification has been developed and used in many applications in the real world. Due to the shared wireless channel between tags and the reader during communication, the tag collision arbitration is a significant issue for reducing the communication overhead. This paper presents a novel anti-collision algorithm named New Enhanced Anti-Collision Algorithm (NEAA) using counters and stack to reduce the probability of collision efficiently and to make it possible to identify multiple passive tags in a timeslot. The upper bound of total timeslots for identifying N passive tags is first derived in this paper; suppose the length of a tag ID is n, the upper bound of total timeslots for identifying N (N= 2n) passive tags is derived to be 2n-1 - n + 4, when n > 2. This bound is quite tight. Compared to the existing methods proposed by other researchers, the performance evaluation shows that the proposed scheme in this paper consumes fewer timeslots and has better performance for identifying tags.