A gearbox for a rack (6) and pinion (4) linear transmission, said gearbox further including—a reduction gear train (1-4) having at least a first (1), a second (2), a third (3), and a fourth gear wheel (4), where the fourth gear wheel is the pinion (4) for rotary engagement with the rack (6); a rotary input shaft (7) operatively connected to the gear train (1-4) to effect a linear relative movement between the rack (6) and the pinion (4); and an intermediate shaft (8) on which the first (1) and the second (2) gear wheel are fixed; the third gear wheel (3) being fixed on the input shaft (7), the fourth gear wheel (4) being journalled to enable it to rotate freely on the input shaft (7) and constituting the pinion (4), and the first gear wheel (1) and the fourth gear wheel (4) being in constant meshing engagement with each other.