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Smoothing fingerprint ridge orientation involves a principal discrepancy. Too little smoothing can result in noisy orientation fields (OF), too much smoothing will harm high curvature areas, especially singular points (SP). In this paper we present a fingerprint ridge orientation model based on Legendre polynomials. The motivation for the proposed method can be found by analysing the almost exclusively used method in literature for orientation smoothing, proposed by Witkin and Kass (1987) more than two decades ago. The main contribution of this paper argues that the vectorial data (sine and cosine data) should be smoothed in a coupled way and the approximation error should not be evaluated employing vectorial data. For evaluating the proposed method we use a Poincare-Index based SP detection algorithm. The experiments show, that in comparison to competing methods the proposed method has improved orientation smoothing capabilities, especially in high curvature areas.