Magnetite was synthesized with $FeSO_4$, and NaOH for the decomposition of carbon dioxide and for the study of the methane formation. The chemical equivalent ratio was changed from 0.5 to 1.50 for the magnetite synthesis. The chemical equivalent ratio was fixed in 1.00, and Nickel chloride and Rhodium chloride equally added and synthesized with the ratio was of 0.10~10.00 mole%. The crystal strucure of the synthesized magnetite was measured XRD. Putting synthesized magnetite in the reactor and using hydrogen gas oxygen-deficient magnetite was made. Injecting carbon dioxide in the reactor, the decomposition reaction was experimented. The formation of methane was confirmed injecting hydrogen gas in the reactor after carbon dioxide was decomposed.