In symmetric key cryptography the sender as well as the receiver possess a common key. Asymmetric key cryptography involves generation of two distinct keys which are used for encryption and decryption correspondingly. The sender converts the original message to cipher text using the public key while the receiver can decipher this using his private key. This is also called Public Key Cryptography. For every public key there can exist only one private key that can decipher the encrypted text. Security of RSA Algorithm can be compromised using mathematical attack, by guessing the factors of a large number. It may also be compromised if one can guess the private key. In accordance with the mathematical attack, we propose a secure algorithm in this paper. In this algorithm, we try to eliminate the distribution of n which is the large number whose factors if found compromises the RSA algorithm. We also present a comparative analysis of the proposed algorithm with the RSA algorithm.