A cutting system for cutting a strip termed a "continuous strip" which extends lengthwise in a direction termed a "longitudinal direction" and widthwise between a first edge and a second edge, said cutting system comprising: - a drive device adapted to drive the continuous strip along a strip path at a speed termed a "forward speed" (V_fwd) that is oriented in the longitudinal direction of said continuous strip, - a first cutting roller that is mounted so as to be able to be driven in a first movement in rotation at a chosen rotation speed about a first rotation axis oriented transversely to the strip path, preferably perpendicularly to said strip path, said first cutting roller being provided with a first helical blade that extends helically around said first rotation axis, said system being characterized by: - a second cutting roller that is mounted to rotate about a second rotation axis, preferably parallel to the first rotation axis, in a second movement in rotation in the opposite direction to the movement in rotation of the first cutting roller and that is adapted to be able, when the continuous strip is engaged between said first and second cutting rollers (20, 30), to cooperate with the first helical blade to cut said continuous strip over all the width of said continuous strip from the first edge to the second edge, and - a variable synchronizer which makes it possible to select and to modify the ratio termed the "synchronization ratio" between the rotation speed of the first cutting roller and the forward speed (V_fwd) of the continuous strip in such a manner as to be able to adjust the angle termed the "cutting angle" (A cut) at which the cut in the continuous strip is oriented relative to the longitudinal direction of said continuous strip. - a drive device adapted to drive the continuous strip along a strip path at a speed termed a "forward speed" (V_fwd) that is oriented in the longitudinal direction of said continuous strip, - a first cutting roller that is mounted so as to be able to be driven in a first movement in rotation at a chosen rotation speed about a first rotation axis oriented transversely to the strip path, preferably perpendicularly to said strip path, said first cutting roller being provided with a first helical blade that extends helically around said first rotation axis, - a second cutting roller that is mounted to rotate about a second rotation axis, preferably parallel to the first rotation axis, in a second movement in rotation in the opposite direction to the movement in rotation of the first cutting roller and that is adapted to be able, when the continuous strip is engaged between said first and second cutting rollers (20, 30), to cooperate with the first helical blade to cut said continuous strip over all the width of said continuous strip from the first edge to the second edge, and - a variable synchronizer which makes it possible to select and to modify the ratio termed the "synchronization ratio" between the rotation speed of the first cutting roller and the forward speed (V_fwd) of the continuous strip in such a manner as to be able to adjust the angle termed the "cutting angle" (A cut) at which the cut in the continuous strip is oriented relative to the longitudinal direction of said continuous strip.