A new mathematical method is developed for interpolation from a given set of data points in a plane and for fitting a smooth curve to the points. This method is devised in such a way that the resultant curve will pass through the given points and will appear smooth and natural. It is based on apiecewise function composed of a set of polynomials, each of degree three, at most, and applicable to successive intervals of the given points. In his method, the slope of the curve is determined at each given point locally, and each polynomial representing a portion of the curve between a pair of given points is determined by the coordinates of and the slopes at the points. Comparison indicates that the curve obtained by this new method is closer to a manually drawn curve than those drawn by other mathematical methods.