Divergence-free　wavelets　are　successfully　applied　to　numerical　solutions　of　Navier-Stokes　equation　and　to　analysis　of　incompressible　flows.　They　closely　depend　on　a　pair　of　one-dimensional　wavelets　with　some　differential　relations.　In　this　paper,　we　point　out　some　restrictions　of　those　wavelets　and　study　scaling　functions　with　the　differential　relation;　Wavelets　and　their　duals　are　discussed;　In　addition　to　the　differential　relation,　we　are　particularly　interested　in　a　class　of　examples　with　the　interpolatory　property;　It　turns　out　there　is　a　connection　between　our　examples　and　Micchelli＇s　work.