A method is provided for the material-removing machining of fillets on a workpiece by means of a tool, more particularly a milling tool, which is guided over a fillet at a contact point. The invention is characterized in that the fillet is machined by means of a tool comprising a conical-convex cutting edge on a flank of the tool, wherein the tool, with the contact point on the conical-convex cutting edge, moves along at least one contact path running in the longitudinal direction of the fillet and the tool is inclined sideways in relation to the at least one contact path on the fillet such that a substantially sickle-shaped material engagement is formed in front of the contact point in the movement direction of the tool.