The present invention relates to a process for purifications of natural or synthetic polymers in solution, water-soluble or soluble in water-alcohol medium and comprising sulfate groups, the process consisting essentially, on the one hand, of a selective precipitation in which the sulfated polymers to be purified are complexed in acid medium with a polyamine insoluble at a pH greater than 7 and, on the other hand, after isolation of the complex thus formed, of a progressive solubilizing of the sulfated polymers.