For interpolating cubic curve, neither by cubic mathematic spline norcubic parameter spline of various kind, it is difficult to possess simultaneo-usly all the characteristics, second order continuity and localization. In thispaper a new method is suggested to construct an interpolating curve with sa-tisfaction for the requirement of characteristics mentioned above. Its outsta-nding feature is that the spline segments of the curve defined locally through4~6 discrete points; and can be adjusted locally witho...