Materials undergoing reversible solid-to-solid martensitic phase transformations are desirable for applications in medical sensors and actuators, eco-friendly refrigerators and energy conversion devices. The ability to pass back and forth through the phase transformation many times without degradation of properties (termed 'reversibility') is critical for these applications. Materials tuned to satisfy a certain geometric compatibility condition have been shown to exhibit high reversibility, measured by low hysteresis and small migration of transformation temperature under cycling. Recently, stronger compatibility conditions called the 'cofactor conditions' have been proposed theoretically to achieve even better reversibility. Here we report the enhanced reversibility and unusual microstructure of the first martensitic material, Zn 45 Au 30 Cu 25, that closely satisfies the cofactor conditions. We observe four striking properties of this material. (1) Despite a transformation strain of 8%, the transformation temperature shifts less than 0.5C after more than 16,000 thermal cycles. For comparison, the transformation temperature of the ubiquitous NiTi alloy shifts up to 20C in the first 20 cycles. (2) The hysteresis remains approximately 2C during this cycling. For comparison, the hysteresis of the NiTi alloy is up to 70C (refs 9, 12). (3) The alloy exhibits an unusual riverine microstructure of martensite not seen in other martensites. (4) Unlike that of typical polycrystal martensites, its microstructure changes drastically in consecutive transformation cycles, whereas macroscopic properties such as transformation temperature and latent heat are nearly reproducible. These results promise a concrete strategy for seeking ultra-reliable martensitic materials.