Abstract: The invention refers to the field of electron beam lithography, in particular to a method for directing an electron beam (6) onto a target position (Z) on the surface of a substrate, the substrate first being placed onto a movable stage (2) and the stage (2) then being displaced stepwise, in the X and/or Y coordinates of a Cartesian grid, until the target position (Z) is located at a spacing from the impact point (P) of the undeflected electron beam (6) which is smaller than the smallest step distance of the stage displacement system, and then the electron beam (6) is directed onto the target position (Z) by deflection. This results in a considerable increase in positioning accuracy in electron beam lithography. Positioning accuracies on the order of 0.1 nm to 0.05 are achievable. The method is suitable in particular for writing grating patterns in which the spacing between the individual grating lines must be maintained with high accuracy.