A non-parametric sequential technique for polygonal approximation of digital curves is proposed. The procedure looks for the longest possible line segments by maximising an objective function which comprises of the length of the line segment and the integral square error along the line segment. The vertices of the polygon are those points where this function attains a local maximum. Though the procedure is sequential and one pass, neither does it round off sharp turnings nor does it dislocate the vertices near the other turnings. © 1994.