A wrapping machine for wrapping a wrapping film around an object. The wrapping machine has a film dispensing unit (1), which comprises first supporting elements (2) for rotatably supporting a first wrapping film reel (3) on the film dispensing unit; first deflecting elements (5.sup.1 . . . 5.sup.10), over which the first wrapping film can be passed to the object to be wrapped; second supporting elements (6) for rotatably supporting a second wrapping film reel (7) on the film dispensing unit; a second deflecting element (9), over which the second wrapping film (8) can be passed. The second deflecting element (9) is mounted on the film dispensing unit (1) so as to be movable between a first position (I) and a second position (II). In position (I), the end of the second wrapping film (8) is in contact with the first wrapping film (4) to cause the first and second wrapping films to adhere to each other during the wrapping process in order to bring them one over the other onto the object to be wrapped. In position (II), the second deflecting element (9) is at a distance from the first wrapping film (4) so that the second wrapping film (9) is clear of contact with and adhesion to the first wrapping film (4). An actuator (10) moves the second deflecting element (9) between the first position (I) and the second position (II). A severing device (11) is arranged to sever the second wrapping film (8) after a desired length of it has been wrapped.