Process of operating an alternating regenerative furnace, said regenerative furnace comprising: - a combustion chamber; - a first set of one or more regenerators; - a second set of one or more regenerators; - one or more fuel injectors (40, 50) for injecting fuel into the combustion chamber, the process comprising: (i) a first operation phase in which (a) the regenerator or regenerators of the first set are in pre-heating mode and preheat cool combustion oxidant and inject hot combustion oxidant into the combustion chamber, in which (b) fuel injected into the combustion chamber by at least one of the one or more fuel injectors (40, 50) combusts with said hot combustion oxidant to produce heat and hot flue gas and in which (c) hot flue gas flows from the combustion chamber into the regenerator or regenerators of the second set which are in heat-recovery mode, and leaves said regenerator or regenerators as cool flue gas, (ii) a second operation phase in which (a) the regenerator or regenerators of the second set are in pre-heating mode and preheat cool combustion oxidant and inject hot combustion oxidant into the combustion chamber, in which (b) fuel injected into the combustion chamber by at least one of the one or more fuel injectors (40, 50) combusts with said hot combustion oxidant to produce heat and hot flue gas and in which (c) hot flue gas flows from the combustion chamber into the regenerator or regenerators of the first set which are in heat-recovery mode, and leaves said regenerator or regenerators as cool flue gas, (iii) a transition phase between successive first and second operation phases and between successive second and first operation phases, in which (a) the regenerator or regenerators (20, 30) which, in the operation phase before the transition phase were in heat-recovery mode inject flue gas into the combustion chamber and in which (b) flue gas flows from the combustion chamber into the regenerator or regenerators (20, 30) which, in the operation phase before the transition phase were in preheating mode, characterized in that: during the transition phase (a) fuel is injected into the combustion chamber by at least one fuel injector (40, 50) of the one or more fuel injectors, and (b), the regenerator or regenerators (20, 30) which, in the operation phase before the transition phase were in heat-recovery mode inject a mixture of flue gas and oxygen-containing gas into the combustion chamber, the mixture having an oxygen content capable of sustaining combustion of the fuel so that the fuel injected by the at least one fuel injectors (40, 50) during the transition phase combusts with the mixture of flue gas and oxygen-containing gas to produce heat and flue gas in the combustion chamber. - a combustion chamber; - a first set of one or more regenerators; - a second set of one or more regenerators; - one or more fuel injectors (40, 50) for injecting fuel into the combustion chamber, (i) a first operation phase in which (a) the regenerator or regenerators of the first set are in pre-heating mode and preheat cool combustion oxidant and inject hot combustion oxidant into the combustion chamber, in which (b) fuel injected into the combustion chamber by at least one of the one or more fuel injectors (40, 50) combusts with said hot combustion oxidant to produce heat and hot flue gas and in which (c) hot flue gas flows from the combustion chamber into the regenerator or regenerators of the second set which are in heat-recovery mode, and leaves said regenerator or regenerators as cool flue gas, (ii) a second operation phase in which (a) the regenerator or regenerators of the second set are in pre-heating mode and preheat cool combustion oxidant and inject hot combustion oxidant into the combustion chamber, in which (b) fuel injected into the combustion chamber by at least one of the one or more fuel injectors (40, 50) combusts with said hot combustion oxidant to produce heat and hot flue gas and in which (c) hot flue gas flows from the combustion chamber into the regenerator or regenerators of the first set which are in heat-recovery mode, and leaves said regenerator or regenerators as cool flue gas, (iii) a transition phase between successive first and second operation phases and between successive second and first operation phases, in which (a) the regenerator or regenerators (20, 30) which, in the operation phase before the transition phase were in heat-recovery mode inject flue gas into the combustion chamber and in which (b) flue gas flows from the combustion chamber into the regenerator or regenerators (20, 30) which, in the operation phase before the transition phase were in preheating mode, during the transition phase (a) fuel is injected into the combustion chamber by at least one fuel injector (40, 50) of the one or more fuel injectors, and (b), the regenerator or regenerators (20, 30) which, in the operation phase before the transition phase were in heat-recovery mode inject a mixture of flue gas and oxygen-containing gas into the combustion chamber, the mixture having an oxygen content capable of sustaining combustion of the fuel so that the fuel injected by the at least one fuel injectors (40, 50) during the transition phase combusts with the mixture of flue gas and oxygen-containing gas to produce heat and flue gas in the combustion chamber.