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Abstract Volcanic rocks, preserving paleorecords of Earth's magnetic field, are essential to constrain the working of the geodynamo, provided their primary signal was not biased. Using a thermomagnetometer, we simulate a situation where a sample's primary record, carried by a thermoremanence (TRM, acquired by cooling in air from 600°C to room temperature), is partly overprinted by a chemical remanence (CRM, acquired by 200 hr of isothermal exposure at 400°C). This situation leads to two directional and intensity components (in the form of linear segments) in the Zijderveld and Arai‐Nagata diagrams. In the case of unstable titanomagnetite grains prior to CRM acquisition, we show that both components can be strongly biased by up to ∼50° for paleodirections and ∼50% for paleointensities. In such a worst‐case scenario, the secondary CRM strongly overprints the primary TRM, rendering the common interpretation of Zijderveld and Arai‐Nagata diagrams in terms of characteristic components invalid.