The present invention concerns a new decationized, dealuminated and stabilized zeolite of L type, characterized particularly by:a total SiO.sub.2 /Al.sub.2 O.sub.3 molar ratio of at least 8,a potassium content lower than 2.9% by weight,parameters a and c of the elementary mesh respectively lower than 1.836 nm and 0.754 nm,a nitrogen adsorption capacity at 77 K, for a partial pressure P/Ps of 0.19, higher than 11% by weight,a benzene adsorption capacity at 30.degree. C., for a partial pressure P/Ps of 0.25, higher than 8.5% by weight, anda lattice of mesopores whose radii, measured by nitrogen adsorption-desorption at 77 K according to the BJH method, range from 0.8 nm to 20 nm.