A new identity is proved that represents the k th order Bsplines as linear combinations of the (k+1) th order B-splines. A new method for degree-raising of Bspline curves is presented based on the identity. The new method can be used for all kinds of Bspline curves, that is, both uniform and arbitrarily nonuniform B-spline curves. When used for degree-raising of a segment of a uniform B-spline curve of degree k-1, it can help obtain a segment of curve of degree k that is still a uniform Bspline curve without raising the multiplicity of any knot. The method for degree- raising of Bezier curves can be regarded as the special case of the new method presented. Moreover, the conventional theory for degree-raising, whose shortcoming has been found, is discussed.