NOVELTY - Carbon dioxide (CO2) fixation apparatus has methane generation unit (1), methane decomposition unit or hydrogen generation unit (HGU), CO2 fixation unit (CFU) and condenser (2). Methane generated in (1) is decomposed in HGU into carbon and hydrogen by catalyst. Hydrogen formed in HGU and CO2 are made to react in presence of catalyst in CFU, to form carbon and water vapor. Water vapor is condensed by (2).    USE - For manufacture of carbon compound such as carbon black sewer time organic refuse and waste treatments and for converting carbondioxide contained in air and exhaust into other substances.    ADVANTAGE - The unreacted gases methane, hydrogen are circulated which results in external energy supply reduction. Since methane decomposition unit, hydrogen generation unit and carbondioxide fixation unit are integrated and the fixation apparatus has a condenser having heat exchange function structure of carbondioxide fixation apparatus is simplified. Ejection of carbon dioxide is prevented (claimed), hence environment is improved and useful carbon compound is obtained as by product. The amount of carbon dioxide gas contained in organic waste is effectively reduced. The energy required for carbondioxide fixation and operating cost are reduced.    DETAILED DESCRIPTION - The carbon dioxide fixation apparatus has (i) anaerobic methane generation unit for generating methane and carbon dioxide from organic waste by fermentation, (ii) methane decomposition unit or hydrogen generation unit (HGU) for decomposing methane into carbon and hydrogen using a catalyst, (iii) carbon dioxide fixation unit for reacting carbondioxide and hydrogen generated by HGU, in the presence of catalyst to form carbon and water vapor and, (iv) condenser for condensing water vapor.    DESCRIPTION OF DRAWING(S) - The figure shows the block diagram of the carbondioxide fixation apparatus.    Methane generation unit (1)    Condenser (2)    Reaction vessel (4)    Catalyst regeneration device (6)    Hydrogen separator (8)