In a method for machining a workpiece by a pulsed laser beam emanating from a tool head, the pulsed laser beam is guided across the workpiece surface in a constant relative position between workpiece and tool head, and the workpiece is machined consecutively in a first and another second relative position. The operating parameters in the second relative position are controlled such that one or more laser pulse hit locations generated in the second relative position have a defined position with reference to one or more laser pulse hit positions generated from the first relative position, particularly lie in a one- or two-dimensional grid defined by plural laser pulse hit positions on the workpiece surface made from the first relative position.