As is well known that the multivariate spline function plays an important role in both theory and application. The paper [1]—[11] hove studied the multivariate spline functions and obtained a lot of results concerning this topic. Especially in [3], the existance theorem has been shown for the case of n-dim entional spline functions. A. Zeniek [10] and P. Alfeld [11] have established some of results about the tetrahedron partition. In this paper. we will show a kind of cubic C—interpolations for any n-simplicial partition in R. Of course, some of the subdivisions will be needed.