An apparatus for conveying sheets from a printing machine to a stack has highly rigid gripper bars that can be produced with relatively little expense, and the gripper assembly permits great flexibility in the use of the apparatus. The apparatus has at least one gripper bar carrying one or more grippers which, during the conveyance, holds a sheet at its edge between a gripper finger and a gripper pad. Endless chains move the gripper bar on a path between a cylinder belonging to the machine and the stack. An actuating mechanism opens and closes the gripper as a sheet is picked up from the cylinder and as it is allowed to fall onto the stack. In the opened state, the gripper finger is located below a path described by the upper edge of the gripper pad.