Alternating regenerative furnace and process of operating an alternating regenerative furnace, in which during the transition phase in which the respective regenerators (20, 30) switch between heat-recovery mode and pre-heating mode and vice-versa, the regenerator or regenerators (20, 30) which before the transition phase were in heat-recovery mode inject a mixture of flue gas and oxygen-containing gas into the combustion chamber (10) of the furnace, which mixture combusts with fuel injected into the combustion chamber (10) to produce heat.