Brazing sheet consisting of a series AA3xxx aluminum alloy core sheet, coated, on at least one side, with a cladding layer made of a first so-called intermediate aluminum alloy containing 0.35 to 1.8 wt % manganese, less than 0.3 wt % of each of other elements, and a total of 1 wt % balance aluminum, itself coated with a second series AA4xxx alloy cladding layer, in which the alloy of the core sheet is selected, and the core sheet developed, such as to have an essentially recrystallized structure after brazing.