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The traditional Random Sample Consensus (RANSAC) algorithm tends to exhibit deficiencies when faced with large amounts of data. In this paper, we present an algorithm called fast Random Sample Consensus (abbr. F-RANSAC) which is able to improve computation efficiency and robustness. We first use the nearest neighbor algorithm to retrieve candidate match points with ranked matching scores. We then construct representative data sets by using a minimal number of optimal matches. Finally, the target homographic matrix is fitted based on the representative data set. Experiments on affine covariant region datasets demonstrate that F-RANSAC significantly enhances computation efficiency(3 times to 10 times) and slightly improves accuracy.