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Presentation of folded documents is not an uncommon case in modern society. Digitizing such documents by capturing them with a smartphone camera can be tricky since a crease can divide the document contents into separate planes. To unfold the document, one could hold the edges potentially obscuring it in a captured image. While there are many geometrical rectification methods, they were usually developed for arbitrary bends and folds. We consider such algorithms and propose a novel approach Unfolder developed specifically for images of documents with a crease from folding in half. Unfolder is robust to projective distortions of the document image and does not fragment the image in the vicinity of a crease after rectification. A new Folded Document Images dataset was created to investigate the rectification accuracy of folded (2, 3, 4, and 8 folds) documents. The dataset includes 1600 images captured when document placed on a table and when held in hand. The Unfolder algorithm allowed for a recognition error rate of 0.33, which is better than the advanced neural network methods DocTr (0.44) and DewarpNet (0.57). The average runtime for Unfolder was only 0.25 s/image on an iPhone XR., Comment: This is a preprint of the article accepted for publication in the journal "Computer Optics"