In this paper we have designed a randomized algorithm to generate a random polygon P from a given set S={p 1 , p 2 ,..., p n } of n points lying on a two dimensional plane. As a preprocessing task, we first compute the convex hull layers from the set S in O(n 2 ) time by modifying the well known Jarvis march algorithm. Next, we execute our algorithm taking the convex hull layers as input to generate random polygons over given point set. This is a Las-Vegas randomized algorithm with O(n ogn)

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... which is much improved over the existing one. We also give a procedure to count the total number of different polygons that can be generated by our algorithm. This number help us to calculate the probability of generating a unique polygon in each execution which measure the randomness of our algorithm.