PURPOSE: To obtain a polyester which is suitable for construction materials and inhibits the generation of smoke and a poisonous gas at burning when molded into a polyurethane foam by reacting a plurality of carboxylic acid(anhydride) components and a polyhydroxyl, etc.

CONSTITUTION: A desired polyester having an acid value of not more than 3 mg KOH/g is obtained by reacting (A) an aromatic component containing four carboxyl groups such as pyromellitic acid, etc., (B) a component being one of (i) 2-16C aliphatic, (ii) 7-16C cyclic non-aromatic and (iii) 8-16C aromatic and containing 2-12 carboxyl groups and (C) an aliphatic, alicyclic or aromatic polyhydroxyl component containing 2-8 hydroxyl groups (e.g. catechol, etc.) and subsequently reacting the reaction product with (D) an alkylene oxide (e.g. ethylene oxide, etc.).