Abstract: A method for obtaining aluminum oxide where the smelted metallurgical slag is subjected to a slow cooling and then self-decomposition by simultaneous action of ultrasound or vibration of high frequency, carried out, which accelerates the formation, in a glassy (vitrous) phase, of a polymorphous, crystalline, high-temperature modification of calcium aluminate, 12 CaO.multidot.7Al.sub.2 O.sub.3, which can be easily lixiviated with aqueous solutions of soda. From lye liquors after extraction, the aluminum oxide is then recovered and the residue, after lixiviation, is burnt to standard portland clinker keeping possibly the lowest proportion of the quantity of clinker produced in relation to the quantity of obtained aluminum oxide.