The invention relates to a device for cutting the human cornea using a focused, pulsed femtosecond laser beam comprises scanner components for adjusting the location 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 are designed to cause a cutting pattern comprising a flap cut (38, 40) to be produced in the cornea when said instructions are executed by the control computer. According to the invention, the cutting pattern further comprises an auxiliary cut (50) that is connected to the flap cut and that leads preferably directly from the flap cut to the cornea surface. The auxiliary cut is advantageously produced before the flap cut and forms a purging channel through which gases that can develop while the flap cut is being cut can escape.