A sheet-processing machine, such as a rotary press, has normally closed grippers that circulate during operation. The grippers transport the sheets along a conveying section and guide the sheets at their leading and trailing edges. The conveying section is assigned a sheet decurler and a sheet guide device that follows the latter in the conveying direction. The conveying section further has a gripper opener assigned thereto for opening the trailing edge grippers carrying the trailing edges of the sheets in order to decurl the sheets. After the sheets have traversed the decurler and decurling has been carried out, the trailing edges are once more grasped with the trailing edge grippers for renewed positive guidance.