A method for calcining mineral rock in a regenerative parallel-flow vertical shaft furnace including the steps of collecting a portion of the gaseous effluent discharged, in preheating mode, from the furnace shaft in a recirculating circuit, forming an oxidizing mixture by mixing the portion collected from the gaseous effluent with concentrated dioxygen from a dioxygen source, and inserting the oxidizing mixture into the top of the shaft in firing mode so as to ensure the combustion of fuel in the presence of oxygen. The gaseous effluent discharged from the furnace having a high concentration of CO.sub.2.