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We present a fast iterative algorithm for identifying the support vectors of a given set of points. Our algorithm works by maintaining a candidate support vector set. It uses a greedy approach to pick points for inclusion in the candidate set. When the addition of a point to the candidate set is blocked because of other points already present in the set, we use a backtracking approach to prune away such points. To speed up convergence we initialize our algorithm with the nearest pair of points from opposite classes. We then use an optimization based approach to increase or prune the candidate support vector set. The algorithm makes repeated passes over the data to satisfy the KKT constraints. The memory requirements of our algorithm scale as O(|SI|/sup 2/) in the average case, where |S| is the size of the support vector set. We show that the algorithm is extremely competitive as compared to other conventional iterative algorithms like SMO and the NPA. We present results on a variety of real life datasets to validate our claims.