The process according to the invention for burning and cooling of carbonate rock takes place in a parallel-flow regenerative lime kiln with two shafts which are operated in alternation as burning shaft and as regenerative shaft, where a. the carbonate rock is added in an upper region designed as preheat and burning zone of each shaft and is preheated and calcined in that region, b. the calcined carbonate rock is then cooled in a lower region designed as cooling zone and having a central deflector in each shaft, c. the cooled calcined carbonate rock is then discharged by way of discharge equipment allocated to each shaft, and where d. cooling air is introduced into the cooling zone to cool the calcined carbonate rock, and is introduced to some extent in the region of the discharge equipment and to some extent by way of the deflector , e. from 90 to 100% of the cooling air to be introduced into the burning shaft is introduced by way of the deflector, at most 10% being introduced in the region of the discharge device, while from 90 to 100% of the cooling air to be introduced into the regeneration shaft is introduced in the region of the discharge equipment, at most 10% being introduced by way of the deflector.