PURPOSE: To obtain the subject substance by transmethylating naphthalene in the presence of dimethylnaphthalenes, producing the monomethyl derivative, simultaneously isomerizing the dimethyl derivative, methylating the monomethyl derivative separated from the reaction mixture and then separating the subject substance.

CONSTITUTION: Naphthalene is transmethylated in the presence of dimethylnaphthalenes (DMN) to produce monomethylnaphthalenes (MMN) and simultaneously isomerize the DMN (at 300-480°C under ordinary pressure to 10atm). Thereby, DMN enriched with the 2,6-DMN and MMN are produced. The resultant product is then separated into naphthalenes, MMN and DMN to methylate the MMN with a transmethylating agent (e.g. xylene) and produce the DMN. Separation into the unreacted MMN, DMN and unreacted transmethylating agent is then carried out. The 2,6-DMN is subsequently separated and recovered from the DMN obtained in the aforementioned two steps. Thereby, the loss of methyl groups is reduced to provide the useful by-products by using the xylenes. As a result, the objective substance is efficiently produced.