The aim of the present paper was to study the kinetics of the isothermal B2 → B19′ transformation in the quaternary Ti_40.7Hf_9.5Ni_44.8Cu₅ shape memory alloy in a wide temperature range to find the common features of this phenomenon in NiTi-based alloys. It was found that the isothermal B2 → B19′ martensitic transformation occurred during holding at a constant temperature both within and outside of the temperature range of the forward transformation. The holding temperature of T* influenced the maximum value of the martensite phase (Φ_M) that appeared under isothermal condition and the rate of the martensite volume fraction variation. The maximum Φ_M value of 80% was found when holding was at T* = M_s (the start temperature of the forward martensitic transformation on cooling), and it was two times larger than in quenched Ni₅₁Ti₄₉ alloy. An increase in holding temperature larger than M_s decreased the maximum Φ_M value and the slope of the Φ_M(t) curve. A decrease in the holding temperature less than M_s decreased the Φ_M value and hardly influenced the dΦ_M/dt value. It was found that the variation in volume fraction of the martensite phase that appeared under isothermal holding at different temperatures in the Ti_40.7Hf_9.5Ni_44.8Cu₅ shape memory alloy was close to the binary Ni₅₁Ti₄₉ alloy, and hence, it was concluded that the features of the kinetics of the isothermal B2 → B19′ transformation were common for this type of transformation in non-stoichiometric NiTi-based alloys.