The present invention provides a topical composition comprising: -A mixture of bioactive sulfated oligosaccharides having a degree of polymerisation (DP) comprised between 2 and 10, and -A physiologically acceptable medium; said oligosaccharides being obtained according to an enzymatic cleavage process according to a β- elimination reaction of polysaccharides extracted from green algae of the ulvagenus comprising aldobiuronic sequences and glucuronan sequences using an ulvan-lyase enzyme adapted to cleave the osidic bond between the units of Glcp A Rhap3 sulfate and between the units Idop A and Rhap3, and using a glucuronan-lyase enzyme adapted to cleave the osidic bond between two Glcp A units. Such a composition has a particularly interesting cosmetic activity on the skin cells, including anti- inflammatory, anti-radical, de-pigmenting effects and effects on molecules of the dermal extracellular matrix (such as collagen 1, collagen 4 and fibronectin), on molecules of the epidermal extracellular matrix (hyaluronic acid). Applications: anti-aging and moisturizing