Thermal aging of the high-temperature shape memory alloy 50.3Ni–29.7Ti–20Hf (at.%) introduces a novel precipitate phase that plays an important role in improving shape memory properties. The precipitate phase was investigated by conventional electron diffraction, high-resolution scanning transmission electron microscopy (STEM) and three-dimensional atom probe tomography. An unrelaxed orthorhombic atomic structural model is proposed based on these observations. This model was subsequently relaxed by ab initio calculations. As a result of the relaxation, atom shuffle displacements occur, which in turn yields improved agreement with the STEM images. The relaxed structure, which is termed the “H phase”, has also been verified to be thermodynamically stable at 0K.