In this paper, we propose a new approach for constructing selectively convertible undeniable signature schemes, and present two efficient schemes based on RSA. Our approach allows a more direct selective conversion than the previous schemes, and the security can be proved formally. Further, our disavowal protocols do not require parallelization techniques to reach a significant soundness probability. Also, our second scheme is the first selectively convertible scheme which is provably secure without random oracles. Keywords. undeniable signature, selective conversion, RSA