This　paper　proposes　a　flexible　frequency　slice　wavelet　transform　(flexible　FSWT)　for　Kurtogram,　a　classic　signal　processing　method,　with　an　intend　to　expand　its　range　of　application.　The　Kurtogram,　however,　does　not　consider　the　details　of　the　spectrum　while　dividing　the　frequency　bands,　which　may　lead　to　diagnosis　errors.　The　variable　window　characteristics　of　the　order　statistic　filter　and　the　minimum　value　spectrum　segmentation　method　have　been　utilized　to　obtain　the　multi-level　spectrum　segmentation　filter　bank,　which　can　be　employed　to　construct　the　basic　framework　of　the　novel　Kurtogram.　Relying　on　the　unrestricted　filtering　property　of　FSWT,　the　reconstruction　and　extraction　of　the　composite　spectrum　boundaries　have　been　realized.　The　flexible　FSWT　adds　self-adaptability　to　the　application　of　FSWT　in　fault　diagnosis,　and　solves　the　problem　of　frequency　band　discrimination　failure　of　time?frequency　diagram　diagnosis.　The　validity　of　flexible　FSWT　has　been　verified　by　simulation　and　experiment　signals.