NOVELTY - Reactants (10) comprising steam and methane is provided into of catalyst-containing reformer tubes (104) in a radiant section of reformer furnace, and reacted. The obtained reformate (12) is withdrawn from the reformer tubes. Fuel gases (74) and oxidant gas mixture (54) are introduced into radiant section externally. The obtained combustion product gas is passed to convection section of reformer furnace. Residual oxygen in portion (B) of the combustion product gas is reacted with hydrogen and methane. Water is removed from portion (B), to obtain carbon dioxide product gas.    USE - Production of carbon dioxide product gas and hydrogen product gas (claimed).    ADVANTAGE - The method enables production of carbon dioxide product gas and hydrogen product gas with high energy efficiency.    DETAILED DESCRIPTION - Reactants comprising steam and methane is provided into of catalyst-containing reformer tubes in a radiant section of a reformer furnace, and reacted in presence of a reforming catalyst under predeterminded reaction conditions, to obtain a reformate comprising hydrogen, carbon monoxide and steam. The reformate is withdrawn from the catalyst-containing reformer tubes where the reformer furnace has a convection section consisting of heat exchange tubes. Fuel gases and oxidant gas mixture comprising 20-35 vol.% oxygen on wet basis are introduced into the radiant section of the reformer furnace externally for combusting the fuel gases with oxygen in the oxidant gas mixture, to obtain combustion product gas. Energy for reacting the reactants inside the catalyst-containing reformer tubes is provided. The combustion product gas from the radiant section of the reformer is passed to convection section. The portion (A) of the combustion product gas is withdrawn from the convection section to the radiant section of the reformer furnace at mass flow rate of 40-60%. Residual oxygen in another portion (B) of the combustion product gas is reacted with hydrogen and methane in the presence of catalyst until oxygen concentration in the portion (B) of the combustion product gas is 10 ppm. Water is removed from the portion (B) of the combustion product, to obtain carbon dioxide product gas. Heat is recovered from reformate from the catalyst-containing reformer tubes for cooling reformate. The cooled reformate is reacted in presence of a shift catalyst under predetermined reaction conditions to shift reformate, to obtain additional hydrogen in reformate. Heat is recovered from the shifted reformate for cooling the shifted reformate. Water is removed from the shifted reformate, to obtain water-depleted reformate comprising hydrogen and secondary gas components. The water-depleted reformate is separated from 3 pressure swing adsorption beds comprising adsorbent for secondary gas components, to obtain hydrogen product gas and pressure swing adsorption tail gas where the fuel gases comprise a portion of pressure swing adsorption tail gas. The portion (C) of combustion product is recycled to prevent leakage of air into the convection section by infiltration through convection section wall(s) and/or the fuel gases are combusted with the oxygen in the oxidant gas mixture in the radiant section under absolute pressure of 102.5-116.3 kPa, to obtain combustion product gas supplying energy for reacting the reactants in the catalyst-containing reformer tubes.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view illustrating Production of carbon dioxide product gas and hydrogen product gas.    Reactants (10)    Reformate (12)    Oxidant gas mixture (54)    Fuel gas (74)    Catalyst-containing reformer tubes (104)