To provide a method for refining in order to reduce or totally eliminate the content of a sulfur compound and the content of an aromatic hydrocarbon composed of a monocyclic ring or a condensed ring in a petroleum fraction after subjecting to super deep desulfurization (hydrodesulfurization).

The method for desulfurizing the sulfur compound and removing the aromatic hydrocarbon contained in the petroleum fraction is carried out as follows. The petroleum fraction obtained by hydrodesulfurizing the petroleum fraction is brought into contact with a γ-butyrolactone solution to provide a solvent layer in a state thereof containing the sulfur compound and the aromatic hydrocarbon contained in the petroleum fraction due to the γ-butyrolactone solution. Naphtha, kerosene or gas oil in which the sulfur compound is desulfurized and the aromatic hydrocarbon is removed is separated as an oil layer. The γ-butyrolactone solution in a state thereof containing the sulfur compound and the aromatic hydrocarbon contained in the petroleum fraction due to the γ-butyrolactone solution is separated and recovered from the solvent layer and recirculated for utilization. The γ-butyrolactone solution in the state thereof containing the sulfur compound and the aromatic hydrocarbon contained in the petroleum fraction is added into a substance of the object of a treatment to be hydrodesulfurized.