A possible method to realize a dispersion-free storage ring is described. The simultaneous use of a magnetic field B and an electric field E in bending regions, where the two fields are set perpendicular to each other, enables us to control the effect of momentum dispersion. When the relation (1+1/γ02)E(ρ)=-v0×B is satisfied for a beam with the velocity v0, the linear dispersion can be completely eliminated all around the ring. It is shown that the acceleration and deceleration induced by the electrostatic deflector counteracts the heating mechanism due to the shearing force from dipole magnets. The dispersion-free system is thus beneficial to producing ultracold beams. It looks probable that the technique will allow one to achieve three-dimensional crystalline beams. At ICR Kyoto University, an ion cooler storage ring SLSR oriented for various beam physics purposes is now under construction. The application of the present idea to S-LSR is discussed and the actual design of the dispersionless bend is given.