Abstract: A method for making a composite extrusion die for making a cellular honeycomb structure with thin cell walls. The method includes the steps of drilling a grid of separate feed holes/channels into an inlet face of an extrusion die base element, and cutting a grid of intersecting primary outlet slots into an outlet face of the base element, where every alternate one of the primary outlet slots is in direct communication with a plurality of the feed channels. Further, the method includes cutting a grid of intersecting secondary outlet slots into the outlet face, where each one of the secondary outlet slots bisects each one of the primary outlet slots. The method further includes scoring a plurality of indentations into that region of the outlet face that does not contain any of the primary and secondary outlet slots, and filling each of the feed channels and each of the primary and secondary outlet slots with a filler material.