A method of increasing proliferation of cells which comprises adding to cells a cellular proliferating amount of a primary hydroxyl group of N-acetylglucosamine selectively desulfated heparin having the following characteristics for an enzyme digestion product of the heparin: (1) contents of unsaturated disaccharides of the following formulae (a) and (b): measured by high performance liquid chromatography in the enzyme digestion product of the selectively desulfated heparin are less than 40% and 30 to 67%, respectively, (2) a content of disaccharides containing an N-substituted sulfate group is 75 to 95%, and (3) the weight average molecular weight Mw is 4,000 to 30,000 dalton.