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The training effect and the hysteresis behaviour of the angular dependence of exchange bias are extensively investigated upon the variation of the IrMn layer thickness tIrMn in a series of Co/IrMn bilayers. When tIrMn is very small, both of them are negligible. Then they increase very sharply with increasing tIrMn and then reach maxima at almost the same value of tIrMn. Finally they both decrease when tIrMn is further increased. The similar variation trends suggest that these phenomena arise from irreversible change of antiferromagnet spin orientations, according to the thermal activation model.