Among the （cubic） splines S（x） interpolating the values （1.2） at the knots（1.1） and satisfying the boundary conditions （1.4）, by the best fitting spline we mean the spline minimizing （1.6）. Its unique existence is wellknown. Here we give an effective and economic way to construct it by geometric considerations in higher dimensional Euclidean spaces but actually by using formulas of interpolatory splines only.