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Most of the certificateless signature schemes are based on elliptic curve and these schemes are inefficient because the pairing operation is very costly to use. In this paper, we propose a new efficient certificateless public key signature scheme without pairing based on the RSA signature and the Schnorr signature. The security of the proposed scheme can be proved to be equivalent to the discrete logarithm problem in the random oracle model. Moreover, compared with the certificateless signature scheme which is built without pairing in Journal of Systems and Software 2009, our scheme requires less computation cost and is significantly more efficient. The new scheme without requiring any public key certificate to verify the public key of each user, solves the key escrow problem in identity-based public key cryptography.