A device for surgery on the human eye includes a pulsed laser apparatus, which is controlled by a control program, that by means of the laser radiation, is capable of generating an incision figure in the cornea that bounds a corneal tissue volume to be removed. The control program is designed such that for the generation of the incision figure the radiation focus is moved successively in s plurality of superposed planes without motion control in the direction of a propagation of the radiation. The control program provides, for each plane, a meandering scan path that, at least in the region of the reversing-points, extends outside the tissue volume. Furthermore, the control program is designed to allow, in each plane, at least such radiation pulses which serve for generating the first incision. Said control program is also designed to blank, in at least a fraction of the planes at least a fraction of those radiation pulses which are assigned to regions of the meandering scan path that are situated at a distance from the first incision.