In this report, we present findings of systematic research on NiCoMnAl alloys, with the purpose of acquiring a higher thermal transformation arrest temperature (T A ). By systematic research, T A in the NiCoMnAl alloy systems was raised up to 190 K, compared to the highest T A of 130 K in NiCoMnIn. For a selected alloy of Ni 40 Co 10 Mn 33 Al 17 , magnetization measurements were performed under a pulsed high magnetic field, and the critical magnetic field-temperature phase diagram was determined. The magnetic phase diagram for Ni 50−x Co x Mn 50−y Al y was also established. Moreover, from the discussion that the formerly called "kinetic arrest phenomenon" has both thermodynamic and kinetic factors, we suggest a terminology change to the "thermal transformation arrest phenomenon".