RFID technology arouses great interests from both its advocates and opponents because of the promising but privacy-threatening nature of low-cost RFID tags. A main privacy concern in RFID systems results from clandestine scanning through which an adversary could conduct silent tracking and inventorying of persons carrying tagged objects. Thus, the most important security requirement in designing RFID protocols is to ensure untraceability of RFID tags by unauthorized parties (even with knowledge of a tag secret due to no physical security of low-cost RFID tags). Previous work in this direction mainly focuses on backward untraceability, requiring that compromise of a tag secret should not help identify the tag from past communication transcripts. However, in this paper, we argue that forward untraceability, i.e., untraceability of future events even with knowledge of a current tag secret, should be considered as an equally or even more important security property in RFID protocol designs. Furthermore, RFID tags may often change hands during their lifetime and thus the problem of tag ownership transfer should be dealt with as another key issue in RFID privacy problems; once ownership of a tag is transferred to another party, the old owner should not be able to read the tag any more. It is rather obvious that complete transfer of tag ownership is possible only if some degree of forward untraceability is provided. We propose a strong and robust RFID authentication protocol satisfying both forward and backward untraceability and enabling complete transfer of tag ownership.