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In this study, we have carried out a laboratory simulation of the low-temperature oxidation (below Tc) of titanomagnetite carrying a primary thermoremanent magnetization (TRM) created in Blab=25-50 µT. The initial material was natural basalt P72/4 from the Red Sea rift zone containing unoxidized (degree of oxidation Z =0) titanomagnetite with ulvöspinel content x=0.5 (Fe2.5Ti0.5O4). Cubic basaltic samples containing titanomagnetite were annealed in air in weak field Ban=50-100 µT at temperature Tan=260 Cfor maximum time t=1300 hours. One group of samples were annealed in the magnetic field perpendicular (Ban⊥TRM) and other parallel (Ban || TRM) to the primary TRM. Thellier's-Coe double-heating method in argon atmosphere were conducted using all samples with different Z. As for Ban || TRM, the calculated field value (Bcalc) obtained from Thellier-Coe’s procedure coincided with the laboratory field (Blab) for all annealing times except t=1300 hours. This result indicates the applicability of the Thellier-Coe method of paleointensity determination on basalt containing titanomagnetite of low and medium degrees of oxidation (Z<0.5). However, inadequate results were obtained from samples annealed in a magnetic field perpendicular to primary TRM(Ban⊥TRM). In this case, the calculated value of the Bcalc field for t=12 hours are overestimated by ~40%, and for t=400 and 1300 hours is underestimated by ~20% relative to the TRM creation field. We conclude that reliability of paleointensity data of oxidized titanomagnetite depends on the direction between magnetic field and TRM during the oxidation process. The work was supported by the Russian Foundation for Basic research under the project no 20-05-00573.