A　subdivision　surface　is　a　method　of　representing　a　smooth,　continuous,　seamless　surface　via　the　specification　of　a　coarser　piecewise　linear　polygon　mesh.　In　this　paper,　we　propose　an　innovative　unified　method　for　constructing　interpolating　subdivisions.　Our　algorithm　extends　the　selected　approximating　subdivision　by　merging　the　merits　of　other　different　interpolating　functions.　By　using　Loop　subdivision　and　Two-point　Linear　interpolation　as　specified　approximating　subdivision　and　difference　interpolating　function　respectively,　the　generated　interpolating　subdivision　is　modified　Butterfly　scheme.　In　addition,　the　Butterfly　subdivision　was　also　used　as　an　instance　of　corresponding　difference　interpolating　function.　A　novel　interpolating　subdivision　scheme,　which　is　named　Loop-Butterfly　scheme　and　refers　to　the　features　of　both　Loop　and　Butterfly　subdivision,　is　introduced　in　this　paper.　The　Loop-Butterfly　subdivision　scheme　can　produce　more　fairing　surface　than　the　Butterfly　subdivision　only　using　the　initial　control　points　for　the　final　interpolation.　The　results　of　our　experiments　reveal　that　our　method　utilizes　the　advantages　of　both　the　approximation　subdivision　method　and　the　difference　interpolating　function.　The　convergence　analysis　verified　that　the　graph　of　Loop-Butterfly　subdivision　is　a　C1　continuous　surface.　©　2013　Binary　Information　Press.