A　class　of　Besov　spaces　are　characterized　by　the　quadratic　and　cubic　Hermite　multiwavelets　(K.　Bittner　and　K.　Urban,　On　interpolatory　divergence-free　wavelets,　Math.　Comp.,　76　(2007),　903-929).　That　characterization　has　a　limitation,　because　of　the　regularity　restriction　of　the　Hermite　splines.　In　this　paper,　we　extend　Bittner　and　Urban＇s　theorem　by　using　B-spline　wavelets　with　weak　duals　introduced　in　the　paper:　R.　Q.　Jia,　J.　Z.　Wang　and　D.　X.　Zhou,　Compactly　supported　wavelet　bases　for　Sobolev　spaces,　Appl.　Comput.　Harmon.　Anal.,　15　(2003),　224-241.