The El Mistikawy and Werle scheme (the EMW scheme) is derived as a member of the family of exponential spline difference schemes. Another member of the family (the IEMW scheme), giving a better accuracy then the EMW scheme is analysed. The truncation error of the IEMW scheme for the polynomials of up to the second degree approaches zero as $\varepsilon$ approaches zero, which is not the case with the EMW scheme. Some numerical results are also presented.