The invention relates to a polyurethane obtainable by reacting a polyisocyanate and a polyol composition comprising a highly branched polysaccharide of randomly bonded glucopyranose units or an alkoxylated derivative of the same. The polysaccharide has an average number of 10 100 glucose residues and said polysaccharide and derivative both have an average functionality of 30 or more. The invention also relates to a process for the production of such a polyurethane as well as a mix for the production of a polyurethane comprising a polyol composition, comprising 2 100 % of a highly branched polysaccharide, at least one catalyst and at least one surfactant.