An image data recording medium is composed of a transparent leader tape, an opaque magnetic tape and a transparent continuous film which are spliced together successively in that order. It is therefore possible to make discrimination between the starting and terminating ends of the magnetic tape from a change from an opaque portion to a transparent portion and the direction of movement of the recording medium without the need to stick pieces of reflecting paper to the magnetic tape. Further, since the magnetic tape is wound up on a reel after the leader tape has been wound thereon, there is no fear of the magnetic tape being deteriorated due to a step which would otherwise be produced in the wound magnetic tape. Also disclosed is a magnetic tape position determining apparatus which comprises a photosensor disposed in opposing relation to the image data recording medium and position determining means for making discrimination between starting and terminating ends of the magnetic tape on the basis of a change in a signal obtained from the photosensor when the recording medium is moved in its longitudinal direction and the direction of movement of the recording medium. Accordingly, it is possible to make discrimination between the starting and terminating ends of the magnetic tape with a simplified arrangement.