A method for producing a rolled product 0.5 to 10 mm thick made from an aluminum alloy comprising, in particular, copper and lithium, in which, after solution annealing and quenching, a short heat treatment is carried out in which the sheet reaches a temperature of between 145° C. and 175° C. for 0.1 to 45 minutes, the speed of heating being between 3 and 600° C./min. The sheet obtained at the end of the method according to the invention has high corrosion resistance and is capable of being shaped for producing a structural element for an aircraft, in particular an aircraft fuselage skin.