The invention concerns a method for making flat thin elements which consists in: producing a zirconium alloy blank also containing, besides the inevitable impurities, 0.8 to 1.3 % of niobium, 1100 to 1800 ppm of oxygen, and 10 to 35 ppm of sulphur; carrying out a beta hardening and hot rolling to obtain a blank and performing on it at least three cold rolling passes with intermediate annealing heat treatments. One of the intermediate heat treatments is performed for a duration of at least 5 hours at a temperature less than 560 DEG C and all the optional treatments subsequent to the long treatment are carried out at a temperature less than 620 DEG C for not more than 15 minutes.