Radio frequency identification (RFID) tag delegation enables a centralized back-end server to delegate the right to identify and authenticate a tag to specified readers. This should be used to mitigate the computational load on the server side and also to solve the issues in terms of latency and dependency on network connectivity. In this study, we describe a basic RFID delegation architecture and then under this model, we investigate the security of an RFID delegation protocol: Song Mitchell delegation (SMD), which is recently proposed by Song and Mitchell. We point out security flaws that have gone unnoticed in the design and present two attacks namely, a tag impersonation attack and a desynchronization attack against it. We also discover a subtle flaw by which a delegated entity can still keep its delegation rights after the expire of them-this infringes security policy of the scheme. More precisely, we show that the protocol will be still vulnerable to previously mentioned attacks, even if the back-end server ends the delegation right of a delegated reader and update the secrets of the delegated tags. To counteract such flaws, we improve the SMD protocol with a stateful variant so that it provides the claimed security properties.