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The transformation of the hysteretic field dependence of the magnetization of a ferromagnetic thin layer in contact with a magnetically hard antiferromagnet is considered. It is shown that this interaction leads to a shift of the hysteresis loop from the configuration symmetric with respect to magnetic field (exchange bias). Furthermore, upon increasing the magnitude of the exchange interaction, within a narrow range of the magnitudes, there occurs a qualitative change in the hysteresis loop shape and its subsequent disappearance; hence the field dependence of the magnetization becomes monotonous and single-valued.