Subdivision　algorithm　defines　a　very　powerful　way　of　constructing　smooth,　continuous,　seamless　surface.　This　paper　proposed　to　construct　families　of　interpolating　subdivision　from　approximating　subdivision　by　combining　an　approximating　scheme　with　a　difference　interpolating　function.　By　combining　Loop　subdivision　with　two-point　linear　interpolation,　the　modified　Butterfly　scheme　is　generated.　Additionally,　a　new　interpolating　subdivision　scheme,　Loop-Butterfly,　was　constructed　by　combining　Loop　subdivision　with　Butterfly　interpolation.　The　results　show　that　the　proposed　method　keeps　the　fairing　surface　of　approximating　schemes.　©　2012　IEEE.