The main aim of this paper is to discuss univalent sense-preserving biharmonic mappings in the unit disk. As a generalization of starlike biharmonic mappings and convex biharmonic mappings, a family of univalent sense-preserving biharmonic mappings   0 , , , BH U    k is given, and it is also given a sufficient condition for a biharmonic mapping in   0 , , ,k  BH U   by using a coefficients inequality. Moreover, it is proved that this coefficients inequality is a characterization of

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... harmonic mappings in the subclass of that with negative coefficients.  0 , , , BH U     k