In order to create, for cement clinker production lines, a calcinator that is connected upstream from the rotary tubular kiln and is equipped with two firings, which enables on the one hand a high-grade calcinated raw meal and on the other hand an exhaust gas with very low NOx emissions, as well as a burning that is as complete as possible of remaining CO-containing NOx reduction zones, it is provided that a combustion point with sub-stoichiometric fuel combustion be arranged both in the rotary kiln exhaust gas ascending line and also in the cooler outgoing air line which form a first and section portion, respectively, of the calcinator and that downstream in a flow direction of the suspension, additional combustion air discharges into the calcinator which combustion air is branched off from the tertiary air line coming from the clinker cooler via at least one branch line.