This paper proposes a new RFID binary tree-based identification protocol, namely Tweaked Binary Tree (TBT), to cope with hidden tag problem caused by capture effect and detection error phenomena. In TBT, the whole identification process is divided into multiple binary tree cycles, and the hidden tags in a cycle are checked and re-transmitted in the first slot of the next one. The average number of slots for a successful detection of a tag, and the tag loss rate, defined as a ratio between the number of missing tags and the whole tag cardinality, are theoretically analyzed. Computer simulations are also performed to validate the theoretical analysis. We also confirm the superiority of the proposed method in comparison with a conventional General Binary Tree (GBT) one.