In RFID (Radio Frequency Identification) system, an anti-collision algorithm plays a prominent role in the tag recognition process to reduce the required time for identifying the tag and enhance the RFID system efficiency. In this paper, we present a theoretical analysis of optimal frame size assignment for the maximization of system efficiency of a tree-based anti-collision algorithm, called optimum dynamic tree (ODT) algorithm, which is used for RFID tag recognition process. Analysis indicates that the appropriate frame size for a given number of competing tags should not be set equal to the number of tags, which is usually adopted in literature. Instead of this, the frame size should be kept smaller roughly by a factor of 0.871 to maximize system efficiency. The closed-form solution for calculating system efficiency has been derived. The simulated results show excellent correlation with the theoretical one. Range for the exact appropriate frame sizes for the number of tags is from 2 to 100. Comparison has been made for the tag-identification time of conventional binary tree and ODT algorithms according to the international standard ISO 18000-6B.