An elevator installation includes an elevator cage, which is movable in an elevator shaft, with a cage door suspension for a cage door, wherein the cage door suspension is movably arranged at the elevator cage by means of at least one movable mount. During operation of the elevator installation, a self-centering aligning movement of the cage door suspension from a skewed setting of the elevator cage, in correspondence with a skew setting axis, to an approximately vertical and centered setting of the cage door suspension in correspondence with a vertical, can be performed.