The invention relates to a method for producing cuts in a transparent material, in particular in the cornea, by creating optical openings in said material by means of laser radiation that is focused in said material, whereby the focal point is displaced in order to produce the cut from a surface grid-type array of optical openings arranged in sequence. The focal point is displaced along a trajectory and optical openings along said trajectory that are adjacent are not produced immediately after one another. In addition, the surface grid-type array of optical openings is constructed from at least two sub-grids, the optical openings of which are processed sequentially grid by grid.