This paper describes a new magnetic method for determining the contribution of weakly magnetic hematite against a strongly magnetic (e.g. magnetite) background. The method involves measurements of Mfr a residual or "final" remanence after hysteretic demagnetization of saturated isothermal remanent magnetization. In terms of sensitivity and precision, our proposed method is superior to the currently popular approach known as the HIRM method. Compared to the latter, Mfr has no error amplification caused by subtraction of terms. The method utilizes the available software for hysteretic demagnetization function on an automated vibrating sample magnetometer (VSM). This, in turn, automatically decreases some of the disturbing effects of the strong magnetic background, e.g., magnetic viscosity, initially non-zero offset of HIRM for partially oxidized magnetite, etc. INDEX TERMS: 1512 Geomagnetism and Paleomagnetism: Environmental magnetism; 1540 Geomagnetism and Paleomagnetism: Rock and mineral magnetism; 1594 Geomagnetism and Paleomagnetism: Instruments and techniques.