In practical applications, the owner of an RFID-tagged item canchange. In this paper, we propose a new RFID ownership transfer protocol using elliptic-curve cryptography. The paper first considers security and privacy requirements in the ownership transfer process. Then the paper provides a detailed description of our ownership transfer scheme outlining various protocol phases. Key features of the proposed scheme are that it allows controlled delegation and authorisation recovery, and the ownership transfer is achieved without a trusted third party. We describe a security analysis of the proposed scheme and demonstrate that it meets the desired security and privacy requirements. We also illustrate the performance results and show that our scheme is feasible for lightweight RFID tags.