A self-climbing system with a self-climbing unit in which the climbing brackets and the working brackets each have anchor receptacles which each correspond with one another in their pattern with respect to their relative positions, with the result that, after freeing the anchor holes, which are used by the working brackets, of an anchor point of a concrete wall section of a concrete building structure, the climbing brackets can be anchored in precisely these freed anchor holes of the anchor point. Moreover, the invention relates to a self-climbing unit for an aforementioned self-climbing system and to a method for moving such a self-climbing unit on a concrete building structure.