The present invention relates to a process for preparing a catalyst which, in a formal sense, comprises 0.1 to 20% by mass of alkali metal and/or alkaline earth metal oxide, 0.1 to 99% by mass of oxide and 0.1 to 99% by mass of silicon dioxide, which is characterized in that it aluminum comprises the steps of treating an aluminosilicate with an aqueous alkali metal and/or alkaline earth metal salt solution under acidic conditions and calcining the aluminosilicate treated with aqueous alkali metal and/or alkaline earth metal salt solution, and to a catalyst which is obtainable by this process and, in a formal sense, comprises alkali metal and/or alkaline earth metal oxide, aluminum oxide and silicon dioxide, which is characterized in that the catalyst, in a formal sense, has a content of alkali metal and/or alkaline earth metal oxides of 0.5 to 20% by mass, a content of aluminum oxide of 4 to 30% by mass and a content of silicon dioxide of 60 to 95% by mass, and to the use of this catalyst in a process for preparing isoolefins having 4 to 6 carbon atoms by catalytic gas phase cleavage of tertiary alcohols or alkyl tert-alkyl ethers.