A thermoform packaging machine including a forming station, a sealing station, a cutting station and a film conveying unit. The film conveying unit includes a clamp chain arranged on a lateral edge of a bottom film, wherein the clamp chain cyclically conveys the bottom film in a direction of production during operation, the bottom film is advanced one cycle length in each cycle of the thermoform packaging machine. Further, the thermoform packaging machine may include a pulling device that pulls a pull section of the bottom film and/or a top film in a direction parallel to the direction of production relative to the lateral edge of the bottom film held by the clamp chain.