Method for manufacturing a rolled product with an aluminium alloy base in particular for the aeronautical industry, successively, a) a bath of liquid metal with an aluminium base is elaborated comprising 2.1 to 3.9% by weight of Cu, 0.6 to 2.0% by weight of Li, 0.1 to 1.0% by weight of Mg, 0 to 0.6% by weight of Ag, 0 to 1% by weight of Zn, at most 0.20% by weight of the sum of Fe and of Si, at least one element from among Zr, Mn, Cr, Sc, Hf and Ti, the quantity of said element, if it is chosen, being 0.05 to 0.18% by weight for Zr, 0.1 to 0.6% by weight for Mn, 0.05 to 0.3% by weight for Cr, 0.02 to 0.2% by weight for Sc, 0.05 to 0.5% by weight for Hf and from 0.01 to 0.15% by weight for Ti, the other elements at most 0.05% by weight each and 0.15% by weight in total, the rest aluminium; b) a rolled slab is cast using said bath of liquid metal; c) optionally, said rolled slab is homogenised; d) said rolled slab is hot rolled and optionally cold rolled into a sheet of a thickness between 0.5 and 10 mm, e) said sheet is solution heat treated and quenched; f) optionally a levelling is carried out and/or said sheet is pulled in a controlled manner with a cumulative deformation of at least 0.5% and less than 3%, g) a short heat treatment is carried out wherein said sheet reaches a temperature between 145°C and 175°C and preferably between 150°C and 170°C for 0.1 to 45 minutes and preferably for 0.5 to 5 minutes, the speed of heating being between 3 and 600°C/min, in which said short heat treatment is carried out in such a way as to obtain an equivalent time at 150°C of 0.5 to 35 minutes and preferably from 1 to 20 minutes, the equivalent time t i at 150°C is defined by the formula: t i = ∫ exp − 16400 / T dt exp − 16400 / T ref where T (in Kelvin) is the instantaneous treatment temperature of the metal, which changes with the time t (in minutes), and T ref is a reference temperature set to 423 K, t i is expressed in minutes, the constant Q/R = 16400 K is derived from the activation energy for the diffusion of the Cu, for which the value Q = 136100 J/mol was used and wherein, the speed of cooling is between 1 and 1000°C/min. a) a bath of liquid metal with an aluminium base is elaborated comprising 2.1 to 3.9% by weight of Cu, 0.6 to 2.0% by weight of Li, 0.1 to 1.0% by weight of Mg, 0 to 0.6% by weight of Ag, 0 to 1% by weight of Zn, at most 0.20% by weight of the sum of Fe and of Si, at least one element from among Zr, Mn, Cr, Sc, Hf and Ti, the quantity of said element, if it is chosen, being 0.05 to 0.18% by weight for Zr, 0.1 to 0.6% by weight for Mn, 0.05 to 0.3% by weight for Cr, 0.02 to 0.2% by weight for Sc, 0.05 to 0.5% by weight for Hf and from 0.01 to 0.15% by weight for Ti, the other elements at most 0.05% by weight each and 0.15% by weight in total, the rest aluminium; b) a rolled slab is cast using said bath of liquid metal; c) optionally, said rolled slab is homogenised; d) said rolled slab is hot rolled and optionally cold rolled into a sheet of a thickness between 0.5 and 10 mm, e) said sheet is solution heat treated and quenched; f) optionally a levelling is carried out and/or said sheet is pulled in a controlled manner with a cumulative deformation of at least 0.5% and less than 3%, g) a short heat treatment is carried out wherein said sheet reaches a temperature between 145°C and 175°C and preferably between 150°C and 170°C for 0.1 to 45 minutes and preferably for 0.5 to 5 minutes, the speed of heating being between 3 and 600°C/min, in which said short heat treatment is carried out in such a way as to obtain an equivalent time at 150°C of 0.5 to 35 minutes and preferably from 1 to 20 minutes, the equivalent time t i at 150°C is defined by the formula: t i = ∫ exp − 16400 / T dt exp − 16400 / T ref where T (in Kelvin) is the instantaneous treatment temperature of the metal, which changes with the time t (in minutes), and T ref is a reference temperature set to 423 K, t i is expressed in minutes, the constant Q/R = 16400 K is derived from the activation energy for the diffusion of the Cu, for which the value Q = 136100 J/mol was used and wherein, the speed of cooling is between 1 and 1000°C/min.