A new bivariate cubic interpolation spline function over triangles is given by the introduction of new interpolation basic functions on triangles , and it possesses continuity and the parameters on the net points can be determined by a transmission formula. In the authors ' opinion , the method in this paper have the advantages of small calculation ,fewer parameters and the parameters can be obtained very easily by using a transmission formula in stead of the Farins' split - triangle interpolante method , thus the new method is easy to use in CAD.