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An algorithm is presented for extending protein models in cases where only a partially built model is available. The problem can be viewed as linking and/or extending the existing separated model fragments in the electron density map. The process of solving this problem is divided into four steps. In the first step, the possible region for the missing part is extracted from an electron density map. For this purpose, the electron density map is first segmented through an electron density threshold value. The segment for the missing part is then isolated by removing the map region of the existing model. In the second step, two anchor positions are located within the isolated segment on the basis of the existing model: one representing the entry of the missing model and the other the exit. In the third step, a set of possible positions for Cα atoms of the extending residue are determined on the basis of the two anchor positions. In the fourth step, the best placement of the residue is found by ranking of the average electron density values. Steps three and four are repeated until all missing residues are built or no further extension is possible. The algorithm has been implemented in the program LAFIRE [Yao, Zhou & Tanaka (2006). Acta Cryst. D62, 189–196], which aims to automate the refinement process, and has been shown to be effective through tests.