In this study, the authors consider certificateless signature (CLS) schemes for strong non-repudiation. They show that previous security models which ensure that any user can have a unique key pair cannot guarantee a CLS scheme to achieve strong non-repudiation. The authors then fix the security model and propose a new CLS scheme which provides strong non-repudiation under the new model, assuming the computational Diffie??Hellman problem is intractable.