Atmospheric resid was treated with N-methylpyrrolidone in the presence of the undecane fraction at mass ratios to the feedstock of 3:1 and 0.5:1 with preliminary light deasphalting with and without pentane. As a result, the sulfur content in the atmospheric resid decrease by four times and the carbon residue decreases by two times. N-Methylpyrrolidone forms an azeotrope with undercane with a boiling point of 179 degrees C. i.e., 25 degrees lower than for the extracting agent. This allows decreasing the degree of its decomposition in regeneration and corrosion of the equipment.