Process for obtaining a hydrocarbon fraction that can be used as a feedstock of an etherification unit and that contains a small amount of diene compounds, nitrogen-containing compounds and sulfur-containing compounds, starting from an initial hydrocarbon feedstock that comprises a mixture of olefins, dienes, and nitrites as well as sulfur-containing compounds, whereby said process comprises at least the following successive stages:

• a) a selective hydrogenation of said initial hydrocarbon feedstock in the presence of a catalyst of group VIII of the periodic table,
• b) a fractionation by distillation of the effluents that are obtained from stage a) under conditions that make it possible to obtain at least two fractions including
  • said hydrocarbon fraction and that comprises a small amount of diene compounds, nitrogen-containing compounds and sulfur-containing compounds, and
  • a heavy fraction that contains heavy hydrocarbons and the majority of the nitrogen-containing compounds and sulfur-containing compounds obtained from the hydrogenation of stage a).