Steganography is the art of passing information in a manner that the very existence of the message is unknown. Steganography is a method of hiding secret messages in a cover object while communication takes place between sender and receiver. Security of confidential information has always been a major issue from the past times to the present time. It has always been the interested topic for researchers to develop secure techniques to send data without revealing it to anyone other than the receiver. Therefore from time to time researchers have developed many techniques to fulfill secure transfer of data and Steganography is one of them. In this paper we have proposed a new technique of image Steganography i.e. Steganography is applied on image edges with RSA algorithm for providing more security to data as well as our data hiding method. The proposed technique uses an ELSB (Edge based least significant bit) technique to generate a pattern for hiding data bits into ELSB of RGB pixel values of the cover image. This technique makes sure that the message has been encrypted before hiding it into a cover image. If in any case the cipher text got revealed from the cover image, the intermediate person other than receiver can't access the message as it is in encrypted form. Objective is not only to prevent the message being read but also to hide its existence. In this paper, canny arithmetic operator has been proved to have good detective effect in the common usage of edge detection. In the algorithm, selfadaptive filter is used to replace the Gaussian filter, morphological thinning is adopted to thin the edge and morphological operator is used to achieved the refining treatment of edge points detection and the single pixel level edge.