A device for machining the human cornea with focused laser radiation includes controllable components for setting the location of the radiation focus, a control computer for controlling these components, and also a control program for the control computer. The control program contains instructions that have been designed to bring about, upon execution by the control computer, the generation of incisions in the cornea in accordance with a predetermined incision figure, the incision figure defining a corneal bed, a flap situated on the bed and also at least one tissue strip situated in the region of the peripheral edge of the flap between the bed and the flap and extending along the edge of the flap. After the flap has been folded away, the tissue strip has to be removed and enables a creaseless post-ablative close fitting of the folded-back flap against the surface of the bed. In this manner, microstriae which may impair the visual capacity can be avoided.