Abstract: The device includes a winding drum (1) on which there is fixed one end of the cord to be wound. This drum includes a smooth portion (8) having a diameter which is greater than the initial diameter of the drum (1), is located at a distance from the cord fixing point (12) and is limited by a shoulder (9). The cord (11) to be wound is guided approximately tangentially to this shoulder so that the turns (11a) formed on the portion of greater diameter are pushed back by the shoulder (9) under the effect of the load, the length of the portion of greater diameter (8) being such that the tension on the cord is zero in the turns (11b) leaving this portion of greater diameter. These loose turns are positioned beside each other on the portion (1) of the drum ensuring an even winding without overlapping of the cord.