A device for machining the human cornea with focused pulsed femtosecond laser radiation comprises scanner components for local setting of the beam focus, a control computer for controlling the scanner components, and a control program for the control computer. The control program contains instructions that upon execution by the control computer are designed to bring about the generation of an incision figure in the cornea encompassing a flap incision (38, 40). In accordance with the invention the incision figure further encompasses an auxiliary incision (50) connected with the flap incision and leading locally, preferentially directly, away from the latter as far as the surface of the cornea. The auxiliary incision is expediently generated temporally ahead of the flap incision and forms a discharge channel through which gases can escape that may arise in the course of the cutting of the flap incision.
