The traditional security notion of proxy re-encryption (PRE) focuses on preventing the proxy learning anything about the encrypted messages. However, such a basic security requirement is clearly not enough for scenarios where the proxy can collude with Bob. A desirable security goal is, therefore, to prevent a malicious proxy colluding with Bob to re-delegate Alice's decryption right. In 2005, Ateniese et al. first proposed this intriguing problem called non-transferability, in the sense that the only way for Bob to transfer Alice's decryption capability is to expose his own secret key. However, no solutions have achieved this property. In this paper, we positively resolve this open problem. In particular, we give the first construction of non-transferable PRE where the attacker is allowed to obtain one pair of keys consisting of Bob's secret key and the corresponding re-encryption key. Using indistinguishability obfuscation and k-unforgeable authentication as main tools, our scheme is provably secure in the standard model. The essential idea behind our approach is to allow Bob's secret key to be evoked in the process of decrypting Alice's ciphertext while hiding the fact that only Bob could decrypt it by the obfuscated program. In addition, we also show a negative result: a CPA secure PRE scheme with ‘error-freeness’ property cannot be non-transferable.