In the hydrocracking process in accordance with the invention, which comprises a hydrocracking section, a high pressure hot separator and a fractionation section, upstream of the fractionation section, a stripper or reboiler column type separation column is added which treats at least a portion of the heavy effluent obtained from the high pressure hot separator. All or a portion of the bottom fraction from said column, which is rich in polynuclear aromatic compounds, is purged. At least a portion of the bottom fraction obtained from the fractionation section, which is constituted by unconverted products, is recycled to the reaction section.