As new generation of high-temperature shape memory alloys, high-entropy alloys (HEAs) have been attracted for strong solid-solution hardened alloys due to their severe lattice distortion and sluggish diffusion. TiPd is the one potential high-temperature shape memory alloys because of its high martensitic transformation temperature above 500 °C. As constituent elements, Zr expected solid-solution hardening, Pt expected increase of transformation temperature, Au expected keeping transformation temperature, and Co expected not to form harmful phase. By changing the alloy composition slightly, two HEAs and two medium entropy alloys (MEAs) were prepared. Only two MEAs, Ti45Zr5Pd25Pt20Au5, and Ti45Zr5Pd25Pt20Co5 had the martensitic transformation. The perfect recovery was obtained in Ti45Zr5Pd25Pt20Co5 during the repeated thermal cyclic test, training, under 200 MPa. On the other hand, the small irrecoverable strain was remained in Ti45Zr5Pd25Pt20Au5 during the training under 150 MPa because of the small solid-solution hardening effect. It indicates that Ti45Zr5Pd25Pt20Co5 is the one possible HT-SMA working between 342 and 450 °C.