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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=50-100μT 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.