Improving the functional stability of shape memory alloys (SMAs), which undergo a reversible martensitic transformation, is critical for their applications and remains a central research theme driving advances in shape memory technology. By using a thin-film composition-spread technique and high-throughput characterization methods, the lattice parameters of quaternary Ti–Ni–Cu–Pd SMAs and the thermal hysteresis are tailored. Novel alloys with near-zero thermal hysteresis, as predicted by the geometric non-linear theory of martensite, are identified. The thin-film results are successfully transferred to bulk materials and near-zero thermal hysteresis is observed for the phase transformation in bulk alloys using the temperature-dependent alternating current potential drop method. A universal behavior of hysteresis versus the middle eigenvalue of the transformation stretch matrix is observed for different alloy systems. Furthermore, significantly improved functional stability, investigated by thermal cycling using differential scanning calorimetry, is found for the quaternary bulk alloy Ti50.2Ni34.4Cu12.3Pd3.1.