A method and a relative unit (1) for producing blister packs (7) by cutting a blister band (4), according to which a band (4) with blisters (2) housing products is fed in a selected feeding direction (A), through subsequent stations: a band (4) verifying station, a closing station where the blister band is closed with a covering band, and to a cutting station (5) for cutting the closed blister band (4). In the cutting station (5), the closed blister band (4) is cut by progressive shearing, to obtain relative blister packs (7) detached from at least one strip (9a, 9b) or scrap longitudinal edge of the blister band (4). If portions of the blister band (4) considered unsatisfactory are detected in the control station, the subsequent shearing is performed partially or incompletely, so as to prevent detachment of the corresponding blister packs (8), considered faulty and destined to be rejected, from the strip (9a, 9b) of the band (4).