NOVELTY - Removing carbon dioxide (CO2) from a feed mixture comprising methane and CO2, involves subjecting the feed mixture to first distillation column at pressure of at least 45 bar to yield first bottom and top product stream; heating first top product stream; subjecting the heated first top product stream to second distillation column at pressure lower than 45 bar to yield second top and bottom product stream; and feeding second bottom product stream to first distillation column.    USE - For removing carbon dioxide (CO2) from feed mixture comprising methane and carbon dioxide, where feed mixture is acid gas, that is, natural gas containing acidic components CO2 and hydrogen sulfide (H2S).    ADVANTAGE - The method allows complete separation of methane also at higher level of acidic components, is economical and does not result in solid CO2 build-up, which is a common problem in cryogenic distillation. The method yields pure stream of methane (purity more than 99 mol.%) as a top stream, while the bottom stream comprising CO2 and other components is recycled back to the first distillation step. Since methane is obtained as a pure stream, the method of the invention is also a method for the separation, or purification, of methane from its mixtures with CO2. The method is suitable for processing acid gas with high amounts of acid components and in the presence of other impurities such as higher hydrocarbons. The process also allows to obtain the acidic components CO2 and H2S at a relatively high pressure in the liquid state as the bottom stream of the high pressure section, which is advantageous for further use, e.g. sequestration. The method is simple and economical as it does not require a third component to be added to the natural gas in order to prevent the build-up of solid carbon dioxide inside the distillation column, which component needs a further step for the separation and recovery. The invention can also he successfully addressed to the purification of biogas to bio-methane because of the high content of carbon dioxide to be removed.    DETAILED DESCRIPTION - Removing carbon dioxide (CO2) from a feed mixture comprising methane and CO2, involves (a) subjecting the feed mixture to a distillation step in a distillation column or its section, at a pressure of at least 45 bar, yielding a bottom product stream comprising CO2 and a top product stream comprising CO2 and methane; (b) heating the top product stream or its part to yield a heated top product stream respectively a heated part of first top product stream, where heating is done to a temperature higher than the dew point of the stream at the pressure of the subsequent second distillation step; (c) subjecting the heated first top product stream or its heated part, respectively, to a second distillation step in a second distillation column or second section of the distillation column, at a pressure lower than 45 bar, yielding a second top product stream comprising methane and second bottom product stream; and (d) feeding second bottom product stream to the first distillation column or first section of the distillation column.