The invention relates to sulphated polysaccharides which have the general structure of the constituent polysaccharides of heparin and which have a molecular weight of less than 8000 Daltons, comprising two antithrombin III-binding hexasaccharide sequences corresponding to formula (I) in which: R1 represents an OH group when the hexasaccharide of formula (I) is located at the reducing end of the polysaccharide, or else R1 represents a bond with another saccharide unit of said polysaccharide; R2 represents a hydrogen atom when the hexasaccharide of formula (I) is located at the non-reducing end of the polysaccharide, in which case the bond between carbon atoms 4 and 5 of the first saccharide unit of said hexasaccharide is a double bond, or else R2 represents a bond with another saccharide unit of said polysaccharide, in which case the bond between carbon atoms 4 and 5 of the first saccharide unit is a single bond. Preparation thereof, use thereof as antithrombotic medicaments, and also use thereof in a method for analyzing a sample of a heparin derivative.