A process whereby scrambled data of the stream are, in parallel with their recording (6), descrambled (2, 3) so as to extract (4) therefrom additional data corresponding to information required by at least one function of the special mode or "trick mode" (fast forward, fast rewind, accelerated motion, slow motion, etc.). These additional data are also recorded (6) on the recording medium. Applications relate most particularly to recordings on hard disk or DVD.