A handling system in a machine for processing containers, including a plurality of support plates circulating in a closed circuit, each support plate including one or more housings, each housing being able to hold a container, a working portion, in which the support plates circulate in a horizontal position, with a first member for moving the support plates along a first axial direction, a rapid return portion, with a second moving member configured to move the support plates along an opposite axial direction, the support plates circulating in the return portion in a vertical return orientation, the handling system including rotation stations for pivoting the support plates.