Ni–Ti–based shape memory alloys (SMAs) have found widespread use in the last 70 years, but improving their functional stability remains a key quest for more robust and advanced applications. Named for their ability to retain their processed shape as a result of a reversible martensitic transformation, SMAs are highly sensitive to compositional variations. Alloying with ternary and quaternary elements to finetune the lattice parameters and the thermal hysteresis of an SMA, therefore, becomes a challenge in materials exploration. Combinatorial materials science allows streamlining of the synthesis process and data management from multiple characterization techniques. In this study, a composition spread of Ni–Ti–Cu–V thin-film library was synthesized by magnetron co-sputtering on a thermally oxidized Si wafer. Composition-dependent phase transformation temperature and microstructure were investigated and determined using high-throughput wavelength dispersive spectroscopy, synchrotron X-ray diffraction, and temperature-dependent resistance measurements. Of the 177 compositions in the materials library, 32 were observed to have shape memory effect, of which five had zero or near-zero thermal hysteresis. These compositions provide flexibility in the operating temperature regimes that they can be used in. A phase map for the quaternary system and correlations of functional properties are discussed with respect to the local microstructure and composition of the thin-film library.