Method for conveying a series of flat objects in the form of rectangular cutouts in a longitudinal direction implemented in a device for the processing and conveying of flat objects from a folder-gluer machine having the function of folding and gluing a series of flat objects in the form of rectangular cutouts, comprising a pivot unit comprising two substantially identical pivot devices (10, 20), disposed following one another in a conveying direction, each pivot device (10, 20) comprising two conveyors (11, 12, 21, 22), the conveyors (11, 12, 21, 22) being disposed parallel to one another in order to convey each cutout by supporting it together and which are able to be moved at different speeds in order to make each cutout pivot by conveying it, which pivot is made over 90°, the device comprising at least one pivot zone of cutouts wherein the cutouts are conveyed by the conveyors (11, 12) at a first longitudinal movement speed (11, 12) and a second zone adjacent to the pivot zone, wherein the second zone, the cutouts are conveyed by the conveyors (21, 22) at a second longitudinal movement speed, each cutout being pivoted while being conveyed at the first longitudinal movement speed during the pivot phase in the pivot zone, wherein each cutout is conveyed at the second longitudinal movement speed in the second zone adjacent to the pivot zone, characterised in that - the second speed is different from the first speed, - each conveyor (11, 12, 21, 22) engages with specific flattening means, the flattening means being provided with at least one suctioning member able to generate a suctioning through the conveyor (11, 12, 21, 22), - if the pivot has the effect that the series of cutouts pass from a longitudinal position in the direction of the conveying to a transverse position, the second speed is less than the first speed, the second zone following the pivot zone in the movement direction of the cutouts, the cutouts entering into the second zone being seized in a fixed manner, the rear part of the cutout which also undergoes a driving in the pivot zone being able to slide over the first conveyors (11, 12) due to a reduction of the suctioning force over the final part of the pivot zone to not shape the cutout, the front part of which is conveyed at a lesser speed, - if the pivot has the effect that the series of cutouts pass from a transverse position in the direction of the conveying to a longitudinal position, the second speed is greater than the first speed, the second zone preceding the pivot zone in the movement direction of the cutouts. - the second speed is different from the first speed, - each conveyor (11, 12, 21, 22) engages with specific flattening means, the flattening means being provided with at least one suctioning member able to generate a suctioning through the conveyor (11, 12, 21, 22), - if the pivot has the effect that the series of cutouts pass from a longitudinal position in the direction of the conveying to a transverse position, the second speed is less than the first speed, the second zone following the pivot zone in the movement direction of the cutouts, the cutouts entering into the second zone being seized in a fixed manner, the rear part of the cutout which also undergoes a driving in the pivot zone being able to slide over the first conveyors (11, 12) due to a reduction of the suctioning force over the final part of the pivot zone to not shape the cutout, the front part of which is conveyed at a lesser speed, - if the pivot has the effect that the series of cutouts pass from a transverse position in the direction of the conveying to a longitudinal position, the second speed is greater than the first speed, the second zone preceding the pivot zone in the movement direction of the cutouts.