Ju et al proposed a certificateless signature scheme with instantaneous revocation by introducing security mediator (SEM) mechanism. This article presents a detailed cryptoanalysis of this scheme and shows that, in their proposed scheme, once a valid signature has been produced, the signer can recover his private key information and the instantaneous revocation property will be damaged. Furthermore, an improved mediated signature scheme, which can eliminate these disadvantages, is proposed, and security proof of the improved scheme under elliptic curve factorization problem (ECFP) assumption and bilinear computational diffie-hellman problem (BCDH) assumption is also proposed.