The present invention relates to a process for converting methane into a liquid mixture of (C 3+ ) alkanes having 3 carbon atoms and more, preferably (C 4+ ) alkanes having 4 carbon atoms and more, especially (C 5+ ) alkanes having 5 carbon atoms and more. It comprises a stage (1) comprising converting methane into acetylene, performed by submitting methane to a thermal cracking reaction, so as to form a reaction mixture (M1) comprising acetylene and hydrogen, a stage (2) comprising converting acetylene into ethane, performed by contacting the acetylene or the reaction mixture (M1) previously obtained with hydrogen in the presence of a hydrogenation catalyst (C1), so as to form a reaction mixture (M2) comprising ethane, a stage (3) comprising simultaneous ethane self- and cross-metathesis reactions performed by contacting the ethane or the reaction mixture (M2) previously obtained with a metal catalyst (C2) capable of producing, in contact with alkane, reactions involving the splitting and recombining of C-C and/or C-H and/or C-metal bonds, so as to form a reaction mixture (M3) comprising methane and a mixture of the (C 3+ ), preferably the (C 4+ ), especially the (C 5+ ) alkanes, and a stage (4) comprising fractionating the reaction mixture (M3) so as to separate and to isolate said mixture in liquid form. Preferably, the methane is also separated in stage (4) and recycled into stage (1) for methane conversion into acetylene