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A number of different approaches have been proposed to predict elemental component formulas (or molecular formulas) of molecular ions in low and medium resolution mass spectra. Most of them rely on isotope patterns, enumerate all possible formulas for an ion, and exclude certain formulas violating chemical constraints. However, these methods cannot be well generalized to the component prediction of fragment ions in tandem mass spectra. In this paper, a new method, FFP (fragment ion formula prediction), is presented to predict elemental component formulas of fragment ions. In the FFP method, the prediction of the best formulas is converted into the minimization of the distance between theoretical and observed isotope patterns. And, then, a novel local search model is proposed to generate a set of candidate formulas efficiently. After the search, FFP applies a new multiconstraint filtering to exclude as many invalid and improbable formulas as possible. FFP is experimentally compared with the previous enumeration methods, and shown to outperform them significantly. The results of this paper can help to improve the reliability of de novo in the identification of peptide sequences.