Sheet processing apparatus including a first tray for stacking sheets received from an image forming apparatus, a discharge unit for discharging the sheets from the first tray in a bundle, a second tray for stacking the sheets discharged from the first tray, a discriminating unit for discriminating an attribute of a sheet to be stacked on the first tray, and a controller for selectively controlling whether or not to discharge sheets by the discharge unit in accordance with a discrimination of the discriminating unit.