The present disclosure relates to a fastening part for a storage system. The system comprises a storage device, such as a basket, a set of hooks, a shoe rack, a perforated panel or the like, which can be attached, by means of the fastening part, to a carrier element with a number of slots. The fastening part comprises a base portion, with at least one opening, an inner part, resting on the base portion at the carrier element's side and providing at least one hook to be inserted into the carrier element, and another part resting on the base portion at an outer side, and comprising a connector that engages with the inner part through said at least one opening, such that the base portion is sandwiched between the inner part and the outer part.