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Super splines are bivariate splines defined on triangulations, where the smoothness enforced at the vertices is larger than the smoothness enforced across the edges. In this paper, the smoothness conditions and conformality conditions for super splines are presented.Three locally supported super splines on type-1 triangulation are presented. Moreover, the criteria to select local bases is also given. By using local supported super spline function, avariation-diminishing operator is built. The approximation properties of the operator are also presented.