This paper on Cipher based on 3D Array Block Rotation is in continuation with our earlier paper titled A cipher based on 3D Array Block Rotation. It discusses a new rotation; lateral shift along with the earlier discussed rotation of the 3D Array block or circular shifting of plates of 3D Array in clockwise direction while enciphering and anticlockwise direction while deciphering. It also discusses the problem of relative bit positioning in the earlier specified algorithm and introduce shift rotations of the blocks as a possible solution to the problem. It uses a key of specified length which can be either transferred with the ciphertext or can be obtained by an agreed upon random bit generator. In all, it is a novel and effective cipher with good randomness property