The invention relates to a process for the removal of CO2 from acid gas by cryogenic distillation performed in two steps. The feed mixture is first distilled at high pressure (at least 45 bar) in a first distillation column. The top product or a part thereof is then, after heating, subjected to a second distillation step at a lower pressure (lower than 45 bar). The top product of the second distillation step is methane of high purity (more than 99 mol. %). The bottom product of the second distillation step is recycled back to the first distillation column. The method according to the invention 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.