A knife has a casing, a blade, and a blade support carrying the blade and movable in the casing between a rear safety position in which the blade is recessed in the casing, a cutting position in which the blade projects forward out of the casing, and a blade-change position forward of the cutting position and in which the blade projects out of the casing to a greater extent than in the cutting position. An actuator can move the blade support, and a latch is slidable into and out of a blocking position fixing the blade support in the blade-change position in a releasable manner.