We test a new inverse Thellier method of paleointensity determination. Instead of heating-cooling steps, it uses cooling-heating steps below room temperature T0 to eliminate chemical alteration, a major cause of failure in the Thellier method. Inverse thermoremanent magnetization (ITRM), produced when magnetite warms from below the Verwey transition (TV = 120 K) to T0 in a field H, is a prime candidate for the inverse Thellier method. ITRM can be produced in nature if the interior of a magnetite-bearing meteorite is <TV at impact and warms in the Earth's field. Other types of natural remanent magnetization (NRM) may be suitable for inverse Thellier treatment if their low-temperature demagnetization (LTD) spectra resemble the ITRM spectrum. In our experiments, NRM was an ITRM produced by warming from 30 K to T0. NRM remaining after the first (zero-field) cooling-warming step to T was compared to partial ITRM (pITRM) produced by H (usually 0.1 mT) in the second step. NRM and pITRM values from T = 200, 150, 130, 120, 110, 100 and 90 K steps give an inverse Arai plot, whose slope is the ratio between the ITRM and pITRM fields. We measured magnetites with mean grain sizes of 0.065, 0.2, 1, 3, 6, 9, 17, 20 and 135 ¿m and two gabbros containing elongated single-domain magnetite. Single-domain samples had quasi-linear inverse Arai plots but other samples had convex-down curves, resembling Arai plots for TRM in multidomain grains. More ITRM is lost in zero-field steps than is regained as pITRM during in-field steps. The reason is that LTD mainly affects domain walls and highlights multidomain behavior. However, the inverse Thellier method may have more linear behavior if the NRM is a TRM because the greater resistance of TRM to LTD should offset the too-rapid decay of ITRM in zero-field steps.