A complementary locking system for locking legs to the deck of a jack-up offshore drilling platform is disabled. The system includes at each leg, at least one assembly comprising plates forming two counter-racks that engage with a leg rack and, on one side of the plates, at least one internal element for connecting the internal edges of the plates, at least one external element for connecting the external edges of the plates and at least one intermediate member for connecting said at least one internal element to said at least one external element. Methods of installing said complementary locking system on the legs of a jack-up offshore drilling platform are also disclosed.