The present invention concerns a device (1) for grinding a seasoning product such as, in particular, salt, a spice or a condiment, by means of a mill (10), said grinding device (1) comprising a bowl (2) of annular appearance and a bulb (3) of frustoconical appearance capable of being rotated in said bowl (2) when the mill (10) is actuated, by means of an axial rod (4) linked to the top (31) of same, the inner face of said bowl (2) and the outer face of said bulb (3) being provided with toothings (20, 32), said grinding device (1) also comprising a flange (6) for rigid connection to said mill (10), said flange (6) having a "U" shape comprising two lateral branches (62, 63) linked by a transverse arm (60), the distance (d) between the two lateral arms (62, 63) being adjusted to the diameter of said bowl. The device is characterised in that it comprises means for aligning the rotational axis of the bulb (3) with the axis of the bowl (2).