A surgical system (1; 1'), comprising first (10; 10') and second (20; 20') elements which are either two surgical implants or a surgical implant and a surgical instrument, wherein the first element (10; 10') includes: - a first bearing face, and - a first helical surface (13; 13') which extends from the first bearing face, and wherein the second element (20; 20') includes: - a second bearing face, which matches the first bearing face, - a second helical surface (31; 31') which extends from the second bearing face and is congruent with the first helical surface (13; 13') so that the first and second helical surfaces form a first helical connection between the first and second elements, centered on an axis (X30; X30'), and - a mechanism for controlling the reversible connection between the first and second elements, characterized in that the mechanism is adapted to be actuated successively: - along a first movement, which is a translation along the axis (X30; X30') without involving rotation about the axis and by which the mechanism mates the first (13; 13') and second helical surfaces (31; 31') with each other until the first and second bearing faces are axially juxtaposed against each other, and - along a second movement, which is a rotation about the axis and by which the mechanism locks the first helical connection while the first and second bearing faces are pressed axially against each other. wherein the first element (10; 10') includes: - a first bearing face, and - a first helical surface (13; 13') which extends from the first bearing face, - a first bearing face, and - a first helical surface (13; 13') which extends from the first bearing face, and wherein the second element (20; 20') includes: - a second bearing face, which matches the first bearing face, - a second helical surface (31; 31') which extends from the second bearing face and is congruent with the first helical surface (13; 13') so that the first and second helical surfaces form a first helical connection between the first and second elements, centered on an axis (X30; X30'), and - a mechanism for controlling the reversible connection between the first and second elements, - a second bearing face, which matches the first bearing face, - a second helical surface (31; 31') which extends from the second bearing face and is congruent with the first helical surface (13; 13') so that the first and second helical surfaces form a first helical connection between the first and second elements, centered on an axis (X30; X30'), and - a mechanism for controlling the reversible connection between the first and second elements, characterized in that the mechanism is adapted to be actuated successively: - along a first movement, which is a translation along the axis (X30; X30') without involving rotation about the axis and by which the mechanism mates the first (13; 13') and second helical surfaces (31; 31') with each other until the first and second bearing faces are axially juxtaposed against each other, and - along a second movement, which is a rotation about the axis and by which the mechanism locks the first helical connection while the first and second bearing faces are pressed axially against each other. - along a first movement, which is a translation along the axis (X30; X30') without involving rotation about the axis and by which the mechanism mates the first (13; 13') and second helical surfaces (31; 31') with each other until the first and second bearing faces are axially juxtaposed against each other, and - along a second movement, which is a rotation about the axis and by which the mechanism locks the first helical connection while the first and second bearing faces are pressed axially against each other.