PURPOSE: To selectively obtain secondary amine at a high conversion rate by allowing ammonia or primary amine to react with carbon monoxide, hydrogen and an olefin compound in the presence of a specific catalyst.

CONSTITUTION: In the presence of a catalyst comprising a source of cationic rhodium (e.g. acetyl acetonate salt), a source of an anion other than halide (e.g. rhodium complex) and, as a support, a polymer of an N-heterocyclic compound (e.g. 2-vinyl pyridine copolymer), ammonia or primary amine is allowed to react with carbon monoxide, hydrogen and an olefin compound (e.g. 2-10C alkene) in a solvent (e.g. 1,4-dioxane) at 125 to 170°C under 2,000 to 10,000 kPa to obtain tertiary amine. Here, from 1 to 50 mol the anion and from 10-8 to 10-1 the polymer support are used against 1 g atoms the rhodium and from 10-6 to 102 g atoms the rhodium is used against 1 mol the olefin compound.