The system comprises a magnetic tape (10), a magnetic-head unit (20) and an actuator (40). The magnetic tape (10) has servo tracks (11-19) containing servo signals. The servo signals have been written with a magnetic head, not shown, having a comparatively large gap length. As a result, the servo signals are recorded deep into the magnetic tape (10). The magnetic-head unit (20) comprises a read head (21) and a write head (22) to inscribe the track (63), the read head following a bounding line (13a) between adjacent servo tracks (13 and 14) in response to the servo signals read from said servo tracks (13 and 14) by the read head (21). The system in accordance with the invention is characterized in that it comprises control means which determine the sequence in which the information tracks (61-68) are written, the read head (21) either following a track (61 or 63) between two respective non-overwritten parts (60 and 62 or 62 and 64) of the magnetic tape (10), or following a track (62 or 64) between two respective overwritten parts (61 and 63 or 63 and 65) of the magnetic tape (10).