Curve approximation by connected series of line segments leads to data compression, which is required for higher level processing of that curve. The approximation process should comply with two contradicting goals: smoothing out the curve and, in the same time, preserving sharp changes in the curve. In this work the concept of the alternating convex hull is introduced and is then used to develop a new method that generate polyline approximation for single-valued digital curves. The suggested method has the ability to deal with closed curves if they decomposed to two single-valued curves. The method is hierarchical in nature, that is, the approximation varies from coarser to finer, using nested alternating upper/lower hulls, to comply with error tolerance specified. Experimental results show the success of the method in achieving the required approximation.