Abstract: A group of banknotes aligned and stacked on a longitudinal axis is positioned at the work station of a banding device by a clamp type gripper that compresses a first longitudinal portion of the group along the direction of the axis, ready to be secured with at least one band of strip material; as the compressive force is applied, parts of the notes forming a second longitudinal portion of the group, not directly compressed by the gripping device, are caused to fan out at the top and bottom ends of this same second portion, and accordingly, the banding device includes a finger and a locating surface impinging respectively on the two ends of the second portion and operating in conjunction to compact and smooth the parts of the banknotes coinciding with these same ends.