A new method is described for the oversulfation of (epi)K5-N-sulfates to obtain (epi)K5-amine-O-oversulfates at extremely high degree of sulfation and for the transformation of these intermediates into new N-acyl-(epi)K5-amine-O-oversulfates basically free of activity on the coagulation parameters and useful in the cosmetic or pharmaceutical field. Also described are pharmaceutical compositions containing, as one of their active ingredients, an (epi)K5-amine-O-oversulfate.