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We propose a new interpolatory subdivision scheme for generating nice-looking curvature-continuous curves of round shapes. The scheme is based on a diffusion of normals. Given a subdivided polyline, the new polyline vertices inserted at the splitting step are updated in order to fit diffused (averaged with appropriate weights) normals. Although the resulting interpolatory subdivision scheme is nonstationary, nonlinear, and nonuniform from the traditional point of view, the scheme is easy to implement because the same simple geometric procedure for generating new vertices is used at each subdivision step. According to our experiments, the scheme is robust and demonstrates very good convergence properties.