A system for fastening a cladding panel includes a base profile and a two-element hanger with an upper element and a bottom element. The upper element has a first lateral wall, a first tongue extending out from the first lateral wall, a first shelf connected to the first lateral wall and a first opening for an adjustment bolt. The bottom element has two lateral walls, a second tongue extending out from one of the two lateral walls, and a second shelf connecting the two lateral walls and having a second opening for the adjustment bolt. The first shelf and the second shelf are connected to each other. The base profile is received in a space defined by the two lateral walls. The first tongue and the second tongue form an angle, and are received in respective installation grooves on a non-visible side of the cladding panel.