A system having a non-duplicatable key and a lock cylinder for the key, in which the radius (4) of the non-toothed edge of the key (1), i.e., the distance between the theoretical rotation center in the key and its non-toothed edges (1a), is smaller than the outside radius (5) of the rotor (3), wherein the non-toothed edge (1a) provides at least one blind recess (7) with the first relatively strong compression spring (9) and a safety tumbler pin (8), which can assume protruding and recessing positions in reference to the blind recess (7) in appropriate combination with the safety counter tumbler pin (10), which is inserted into the seat of the stator (2) and spring-loaded by a second relatively weak compression spring (11), wherein the contact between the safety tumbler pin (8) and the safety counter tumbler pin (10) is achieved through an opening (13) that exists in the additional plate (12), which is inserted into the rotor (3), wherein the thickness of the plate (12) equals the difference between the radius (4) of the non-toothed edge of the key and the outside radius (5) of the rotor.