Magnetization isotherms of the Fe 64 Ni 36 Invar alloy have been measured under pressure up to 5.3 GPa in magnetic field up to 5 T using a diamond anvil cell and SQUID magnetometer. The unambiguous change of the pressure parameter dlnM S /dP (from − 9 to − 13 × 10 −2 GPa −1 ) has been observed in a narrow pressure interval from 2.5 to 3.5 GPa at all temperatures in the range from 5 to 300 K. The pressure interval, where the sharp decrease in magnetization was observed, coincides with the critical pressures of the pressure-induced decrease in Fe-moment that were determined by the X-ray Magnetic Circular Dichroism and the X-ray Emission Spectra studies, recently. The pronounced decrease in the Curie temperature of the Fe 64 Ni 36 alloy under pressure, dT C /dP = − 44 ± 2 K/GPa, has been confirmed.