Device for pulling and straightening a metallic monofilament comprising: - upstream and downstream traction systems, the upstream traction system being positioned upstream of the downstream traction system in the direction in which the metallic monofilament progresses, - a system for straightening the metallic monofilament, which system is positioned between the upstream and downstream traction systems, in which device each upstream and downstream traction system respectively comprises an upstream spool and a downstream spool designed to pull the metallic monofilament, each upstream and downstream spool comprising a straight cylindrical body onto which to wind the metallic monofilament, these respectively having an upstream diameter D1 and a downstream diameter D2, the device being arranged in such a way that, in operation, the upstream and downstream circumferential velocities V1 and V2 of each upstream and downstream spool respectively are such that 1 ≤ V2/V1 ≤ 1.02 the device comprising a downstream deflection pulley deflecting the metallic monofilament from the downstream spool back towards the downstream spool, the downstream spool and the downstream deflection pulley being arranged in such a way that the metallic monofilament becomes wound at least once in succession partially around the straight cylindrical body of the downstream spool and partially around the downstream deflection pulley, characterized in that: the upstream and downstream spools are capable of rotating about distinct respective upstream and downstream axes of rotation, each upstream and downstream deflection pulley being capable of rotating about distinct respective upstream and downstream axes of rotation. - upstream and downstream traction systems, the upstream traction system being positioned upstream of the downstream traction system in the direction in which the metallic monofilament progresses, - a system for straightening the metallic monofilament, which system is positioned between the upstream and downstream traction systems, in which device each upstream and downstream traction system respectively comprises an upstream spool and a downstream spool designed to pull the metallic monofilament, each upstream and downstream spool comprising a straight cylindrical body onto which to wind the metallic monofilament, these respectively having an upstream diameter D1 and a downstream diameter D2, the device being arranged in such a way that, in operation, the upstream and downstream circumferential velocities V1 and V2 of each upstream and downstream spool respectively are such that 1 ≤ V2/V1 ≤ 1.02 the device comprising a downstream deflection pulley deflecting the metallic monofilament from the downstream spool back towards the downstream spool, the downstream spool and the downstream deflection pulley being arranged in such a way that the metallic monofilament becomes wound at least once in succession partially around the straight cylindrical body of the downstream spool and partially around the downstream deflection pulley, characterized in that: the upstream and downstream spools are capable of rotating about distinct respective upstream and downstream axes of rotation, each upstream and downstream deflection pulley being capable of rotating about distinct respective upstream and downstream axes of rotation. the upstream and downstream spools are capable of rotating about distinct respective upstream and downstream axes of rotation, each upstream and downstream deflection pulley being capable of rotating about distinct respective upstream and downstream axes of rotation.