ABSTRACT As we all know, security is an integral part of every technology and implementation today. In this IT driven society, cryptography is perhaps the most widespread form of secure communication. Authentication using RSA and chaotic map is basically the mechanism to help in establishing the proof of identities. The baker's map is used for generating random number. Chaos refers to a type of complex dynamical behavior that possesses some special features such as being extremely sensitive to small variations in initial conditions. The project is to make a scheme based on RSA and chaotic map to show that a strong certificate less signature scheme not only keeps the original security properties of the signature, i.e., integrity, authentication and non-repudiation, but also can protect the signer even if the attacker has strong power. In 2014, Chin-Chen Chang, Chin-Yu Sun, and Shih-Chang Chang has given a simmilar designed certificateless-based signature scheme based on RSA operations; however, their scheme is modified and made more secure in this paper so that security level increases. This paper is an improved version to make the RSA-based certificateless scheme stronger and more secure