The invention relates to a cement clinker manufacturing method implemented in a continuous production facility (1) having at least one area (2, 2') for fuel combustion for firing an inorganic raw material. In said method, the raw material is converted into clinker by firing, thus obtaining hot clinker (3), then the hot clinker (3) is cooled in two consecutive steps: a first cooling step, implemented in a first cooler (4); and a second cooling step, implemented in a second cooler (5). According to the invention, the first cooling step is continually carried out by blowing an oxygen gas (6) on the hot clinker to obtain partially cooled clinker, and all the heated oxygen gas (7), created by the first cooler (4), is sent to said at least one combustion area (2, 2') of said facility to be used as a combustion gas by adjusting the amount of oxygen gas, blown in the first cooler, such as to cover the combustion gas needs of said facility without any excess; and the partially cooled clinker (31) is stored in a storage chamber of the second cooler (5) or even a storage chamber associated with said second cooler, and the second cooling step is intermittently carried out on the partially cooled clinker.