We investigated the minor M-H loop focussing especially on the third harmonic component in the loop and its DC-bias magnetic field for a sintered Y-Ba-Cu-O superconductor disk. We found that; (1) the minor loop is a Rayleigh type, (2) the Rayleigh constant depends on the DC-bias field and shows a singular magnetic hysteresis, and (3) the hysteresis is symmetrical when the sample is cooled under zero-magnetic field, whereas it is asymmetric when it is cooled under a magnetic field. These phenomena are qualitatively explainable using the critical state model.