Abstract: A floating support for a tape cartridge inserted into a tape drive, the floating support holding a magnetic head and resiliently supported off stationary structure in the tape drive. The floating support resiliently clamps portions of the cartridge against stationary portions of the tape drive which sets the reference positions of the cartridge with respect to the magnetic head. The floating support prevents the transmission of unwanted forces to the magnetic head support structure which would otherwise end to deform such structure. A floating bridge holding a magnetic head is provided having three leaf springs which engage a bottom wall of a tape cartridge to resiliently clamp the bridge to the cartridge to set the corresponding zenith and azimuth references for the magnetic head. The floating references also makes it possible to separate the cartridge fixing points and the cartridge reference points, in order to make the cartridge holding less sensitive to shock and vibrations.