The invention relates in particular to an unprocessed extruded product for manufacturing a machined extruded product for the aeronautical industry, made of an Al-Cu-Li alloy with the following composition, as weight percentages: Cu: 2.0 - 6.0; Li: 0.5 - 2.0; Mg: 0 - 1.0; Ag: 0 - 0.7; Zn 0 - 1.0; and at least one element selected among Zr, Mn, Cr, Se, Hf and Ti, the amount of said element, if chosen, being 0.05 to 0.20 wt % for Zr, 0.05 to 0.8 wt % for Mn, 0.05 to 0.3 wt % for Cr and for Se, 0.05 to 0.5 wt % for Hf and 0.01 to 0.15 wt % for Ti, Si <= 0.1; Fe <= 0.1; others <= 0.05 each and <= 0.15 in total, the balance being aluminium, having an unprocessed core (21) with an aspect ratio of at least 5 and at least one unprocessed flank (22) with an aspect ratio of less than 4 and in which the length direction is substantially perpendicular to the lengthwise direction of the core, characterized in that a portion of the unprocessed flank (22) connecting the unprocessed flank to the unprocessed core has decreasing thickness and in that the ratio of the thickness of said unprocessed flank (22) at the end of said unprocessed flank connected to the web (E221) to that at the end thereof opposite the core (E222) - i.e. E221/E222 - is less than 0.8, thus defining two substantially symmetrical concave areas.; The invention also relates to the method for manufacturing a machined extruded product and to the corresponding machined extruded product. The products according to the invention are useful in particular for manufacturing floor beams and girders.