The relationship between the acidic property and the composition of a zeolite was precisely measured using Y- and mordenite-type samples with high aluminum contents. The ammonium form zeolite was evacuated and heated to yield the hydrogen form, and subsequently, the ammonia adsorption and temperature-programmed desorption were carried out in-situ without exposure of the hydrogen form sample to humid atmosphere. The number of the desorbed ammonia, showing the acid amount, was approximately same to the number of [Al] -[Na] atoms over the experimental range. This is quite different from the conventionally observed relationship between the acidic propel-ty and composition, in which the acidity is absent at the high aluminum concentration where the secondary-neighboring aluminum species (Al-O-Si-O-Al) is formed. On the basis of the X-ray diffraction, it is suggested that the lack of acidity on the hydrogen form zeolite with high aluminum concentration is due to the destruction of crystal structure, which is induced by exposure of the hydrogen form sample to humidity after removal of ammonia. It is pointed out that the isomorphously substituted aluminum in zeolite generates the acid site according to the stoichiometry even when the aluminum atoms locate the secondary-neighboring sites.