the overall organic layer may be suitably determined in accordance with the sulfuric acid concentration and the molecular weight and molecular weight distribution of the intended polether polyol to be fractionally extracted regarding the aqueous sulfuric acid solution when the method of the present invention is applied to polyether polyol or its product obtained by the use of a cationic polymerization catalyst not containing sulfuric acid then a separately prepared aqueous sulfuric acid solution is used and circulated but when it is applied to polyether polyol obtained by the use of a typical sulfuric acid based cationic polymerization catalyst such as fluorosulfonic acid chlorosulfonic acid or fuming sulfuric acid or other sulfuric acid based catalyst that consists essentially of any of these then sulfuric acid that is derived from the catalyst through degradation thereof with water added after polymerization termination may be used directly as it is accordingly the fractional extraction operation may be carried out in a reaction tank of the polyether polyol or a separatory tank for the recovery of the aqueous sulfuric acid solution after the reaction the fractional extraction in the method of the present invention is effected by stirring the system at a predetermined temperature until the overall organic layer and the aqueous sulfuric acid layer can entirely reach the fractionation equilibrium and then statically leaving it for liquid liquid separation the temperature may be from a room temperature to 100 u00b0 c preferably from a room.