Clenshaw and Negus [1] defined the cubic X-spline, and they applied it to an interpolation problem. In the present paper, for the same interpolation problem, an interpolating splinew is considered by combining two specialX-splines. The construction ofw is such that the computational labour for its determination, in the case of piecewise equally spaced knots, is less than that of the conventional cubic splines c . A complete error analysis ofw is done. One of the main results is that, in the case of piecewise equally spaced knots,w ands c have essentially the same error estimates.