A modified quadruple bend achromat (QBA) optics as a lattice for a low emittance storage ring is presented. The novel feature of this lattice is the use of horizontally defocusing bending magnets with different bending angles to keep the radiation integrals low. A realistic storage ring with six achromats, non-dispersive straight sections of 4.6 m each and a total circumference of 124.8 m is studied. At an energy of 2.5 GeV the emittance yields only 20 pi nm rad. The chromaticities and the sextupole strengths are moderate, the dynamic aperture is large and the momentum acceptance is more than +/-9% relative. A similar 3 GeV storage ring with 12 achromats and a circumference of 300 m yields an emittance of 3 pi nm rad. Possible applications and extensions of the QBA structure for diffraction limited storage rings are discussed.