The apparatus has an input pocket into which a stack of sheets is inserted. At least the sheet to be picked from the stack by the picking device is transported by means of a feed device to a picking device which then picks one sheet from the stack at a time. To improve singling quality, a presingling device is provided which first transports only part of the stack to the picking device. In order to ensure that stacks of different-sized sheet material are singled reliably, an aligning device is provided which transports at least the sheet to be picked from the stack in the direction of a defined stop and thus aligns the sheet against said stop. The aligning device preferably cooperates alternatingly with the feed device. To increase singling reliability, a pressure plate is provided in the presingling device for acting upon the presingled partial stack with a certain pressure.