An apparatus for cutting a flap in the cornea of an eye (10) exhibits the following: a laser radiation source for generating laser radiation, means for shaping and guiding the laser radiation in relation to the cornea (20) in such a manner that in the cornea an incision (28) arises which enables a folding of the flap (26) upwards from the cornea. In the process the incision (28) is guided in the hinge region (22) of the cornea in such a way that an undercut arises under the hinge region (22). By this means it is ensured that, in particular in the case of an fs LASIK, the intervention into the stroma is effected substantially symmetrically in relation to a central axis of the cornea (20), so that no undesirable deformations of the cornea result post-operatively by reason of the intraocular pressure.
