The invention relates to a perforator for performing perforations (5) on a moving paper (1) in its direction of movement. The perforator comprises a perforating tool (3), which has a perforating position, in which the paper is perforated, and a neutral position, in which the paper is not perforated, and a control apparatus, by means of which the perforating tool is optionally set either in perforating position or neutral position. The invention is usable for instance for perforating paper sheets printed out from a printer. The arrangement in accordance with the invention allows the same paper to be consistently used in the printer, while selectively producing perforation merely on the desired sheets.