In the present work the authors have introduced a new advanced symmetric key cryptographic method called NJJSAA. The authors introduced new bit manipulation method for data encryption and decryption of any file. Nath et al already developed some symmetric key methods[1,2,3,4] where they have used some randomized key matrix for encryption and decryption methods. In the present work the authors have used a bit manipulation method which include bit exchange, right shift and XOR operation on the incoming bits. To exchange bits the authors used a randomized key matrix of size (16x16) using the method developed by Nath et al(1). The present method allows the multiple encryption and multiple decryption. To initiate the encryption process a user has to enter a text-key which may be maximum of 16 characters long. From the text-key the authors have calculated randomization number and the encryption number. The method used was developed by Nath et al(1). A slight change in the text-key will change the randomization number and the encryption number quite a lot. Multiple encryption using bit exchange, bit right shift and XOR operations makes the system very secured. The present method is a block cipher method and it can be applied to encrypt data in sensor network or in mobile network. The advantage of the present method is that one can apply this method on top of any other standard algorithm such as DES, AES or RSA. The method is suitable to encrypt any large or small file. There is a scope to further enhance the present method of encryption.