The inner and outer rings of the flexible thin-wall bearing（FTB）are ellipses，and its vibration characteristics are completely different from those of the ordinary rolling bearing. The long and short axes of the ellipse will cause periodic impact on the FTB during the rotation of the bearing，this normal periodic impact and the fault periodic impact caused by the damage of the bearing elements are mixed together，and the fault periodic impact is completely masked. In this paper，the frequency distribution of the normal periodic impact is analyzed，and the singular value decomposition（SVD）is proposed to eliminate this normal periodic impact based on the intrinsic relationship between singular value and frequency. The singular values corresponding to the frequencies of the normal periodic impact are selected for SVD reconstruction，and the normal periodic impact can be accurately separated， thus eliminating its interference to the fault periodic impact. On this basis，the continuous Morlet wavelet transform is used to extract the fault impact feature of the vibration signal in which the normal periodic impact is eliminated，the fault impact feature of the FTB is clearly extracted by selecting the scale with the maximum kurtosis as the fault feature scale，and the effect is much better than that of the case in which the normal periodic impact background is not eliminated