A unit (1) for cutting a continuous web into parallel strips, comprising a first and a second roller (2a, 2b) between which a continuous web is fed and each of which is provided with a succession of circumferential protrusions and recesses alternated with each other along the axis of rotation (X, Y) of the roller (2a, 2b). The rollers (2a, 2b) are coupled to each other so that the protrusions of one roller (2a) are at least partly inserted into the recesses of the other roller (2b) and vice versa, so that the rollers (2a, 2b) cut the continuous web along parallel longitudinal lines. The unit (1) is characterized in that it also comprises cleaning means configured to promote removal of particles of material released in the recesses by the web during cutting.
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