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In this paper, we present a recursive algorithm for piecewise polygonal approximation of a digital curves. The idea behind is to look for an optimal solution while approximating the given curve segment with a set of longest and minimum line segments such that the maximum squared error is less than the given threshold. The given curve is divided into pieces and parallel processing can be applied to each piece of curve thus making it computationally more efficient. Experimental results show that the proposed method has promising results.