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Certificateless cryptography shares many features of identity-based cryptography and partially solves the problem of key escrow. Three certificateless signature schemes without random oracles were found in the literature. However, all the schemes suffer from some common drawbacks. First, by obtaining a signature on a message and replacing the public key of a signer, an adversary can forge valid signatures on the same message under the replaced public key. Secondly, all the schemes require a relatively large size of public parameters. The authors propose a new certificateless signature scheme, which exhibits an improvement on the existing schemes. Compared with the previous schemes, the proposed scheme offers stronger security, shorter system parameters and higher computational efficiency.