Graphical passwords using images have been developed to solve problems in text based password recognition. The basic recognition process scheme of graphical passwords is clicking certain points on the screen image in correct order. In this pre-developed method of graphical passwords the recognition will fail if the precise positions are not clicked. A new graphical password system called PassPositions is introduced in this paper. PassPositions is a new graphical password scheme which is using relative positions never used earlier graphical password schemes. PassPositions is a graphical password scheme based on universal design that everybody can use conveniently without regarding their physical conditions.