Ti–(Zr, Hf)–Ni alloys, in which Zr or Hf is added to Ti–Ni shape memory alloys, are expected to be excellent high temperature shape memory alloys because they have martensitic transformation temperatures above 100°C and high strength at elevated temperatures by utilizing H-phase precipitation. However, during reorientation of martensite variants, deformation stress increases with applied strain without showing a plateau region, making it difficult to obtain a large shape recovery strain. In the martensite phase of Ti–(Zr, Hf)–Ni alloys, thin and dense (001)B19′ compound twins are introduced during the martensitic transformation, and the detwinning of martensite variants becomes difficult to occur, resulting in the increase in deformation stress during the variant reorientation. Therefore, we propose a new alloy-design concept to control the crystal structure by adding a fourth element in order to facilitate detwinning. In this paper, we first considered the cause of (001)B19′ compound twinning in Ti–(Zr, Hf)–Ni alloys, and then selected Pd as the fourth element to change the crystal structure for preventing the formation of (001)B19′ compound twins. Experimental investigations of the effects of alloy composition on the crystal structure, transformation temperatures, and precipitate formation realized this alloy-design concept through presenting a candidate composition range of Ti–(15–20)Zr–49.7Pd and surrounding Ni-containing alloys for new high temperature shape memory alloys which readily undergo detwinning.