This system makes it possible to join a substantially flat base of an element to be fixed to a top plate. It is provided with: at least one hole of elongated shape made in the top plate, a shaft extending substantially perpendicular to the base of the element to be fixed and mounted movable in rotation relative to its longitudinal axis, a fixation head of elongated shape matched to the shape of the hole made in the top plate and disposed on a first side of the base of the element to be fixed, control means for making the shaft pivot around its axis and disposed, relative to the fixation head, on the other side of the base of the element to be fixed.