Bystudyingmodularinvariancepropertiesofsomecharacteristicforms,wegetsomegen-eralizedanomalycancellationformulason（4r-1）-dimensionalmanifoldswithnoassumptionthatthe3rdde-Rhamcohomologyofmanifoldsvanishes.Theseanomalycancellationformulasgeneralizeourpreviousanomalycancellationformulason（4r-1）-dimensionalmanifolds.Wealsogeneralizeourpreviousanomalycancellationformulason（4r-1）-dimensionalmanifoldsandtheHauYurigiditytheoremtothe（a,b）case.
