Process for calcining mineral rock in a regenerative parallel-flow vertical shaft furnace, containing at least two shafts (1, 2) interconnected by a gas transfer channel (3), each shaft operating alternately in firing mode and in preheating mode, the firing mode comprising a combustion of fuel in the presence of air so as to obtain a firing of the rock to give calcined rock, an emission of combustion gases, and a passage of these gases from one shaft to the other by means of said channel (3), the preheating mode comprising a heat exchange between said rock and said combustion gases from said channel (3), this process additionally comprising an injection of supplementary air into said channel (3) with oxidation of unburnt products contained in the combustion gases passing through this channel.