A method for producing cement clinker in a plant that includes: a first cyclone preheater and a second cyclone preheater for preheating first and second portions of a raw material, respectively; a precalcinator using a combustion gas for burning a fuel, the fumes released by the precalcinator being directed to the second cyclone preheater; a rotary furnace provided with a fuel burner, the fumes released by the rotary furnace being directed to the first cyclone preheater; and a clinker cooler that blows cooling air across the clinker at the outlet of the rotary furnace. According to the method, the precalcinator combustion gas contains between 90 and 100 vol % of oxygen. The precalcinator may consist of a fluidized bed, the fluidization gas being the combustion gas. The invention also relates to a plant as such.