The invention concerns a process to manufacture a flat-rolled product, notably for the aeronautic industry containing aluminum alloy, in which, notably a flattening and/or stretching is performed with a cumulated deformation of at least 0.5% and less than 3% and a short heat-treatment is performed in which the sheet reaches a temperature between 130° C. and 170° C. for a period of 0.1 to 13 hours. The invention notably makes it possible to simplify the forming process of fuselage skins and to improve the balance between static mechanical strength properties and damage tolerance properties.