Replayable chosen ciphertext (RCCA) security was introduced by Canetti, Krawczyk, and Nielsen (CRYPTO'03) in order to handle an encryption scheme that is “non-malleable except tampering which preserves the plaintext.” RCCA security is a relaxation of CCA security and a useful security notion for many practical applications such as authentication and key exchange. Canetti et al. defined non-malleability against RCCA (NM-RCCA), indistinguishability against RCCA (IND-RCCA), and universal composability against RCCA (UC-RCCA). Moreover, they proved that these three security notions are equivalent when considering a PKE scheme whose plaintext space is super-polynomially large. Among these three security notions, NM-RCCA seems to play the central role since RCCA security was introduced in order to capture “non-malleability except tampering which preserves the plaintext.” However, their definition of NM-RCCA is not a natural extension of that of original non-malleability, and it is not clear whether their NM-RCCA captures the requirement of original non-malleability. In this paper, we propose definitions of indistinguishability-based and simulation-based non-malleability against RCCA by extending definitions of original non-malleability. We then prove that these two notions of non-malleability and IND-RCCA are equivalent regardless of the size of plaintext space of PKE schemes.