The present invention relates to a polysaccharide having functional groups, wherein said groups are aldehyde groups formed at positions C2 and/or C3 as well as at position C6 of the anhydroglucose units of the polysaccharide chain. Preferably the polysaccharide is a cellulosic fibrous material whose primary and secondary hydroxyl groups of the cellulose are oxidized into aldehyde groups at least in part by means of TEMPO oxidation and periodate oxidation. The invention also concerns a paper or nonwoven comprising the above polysacaride. According to the invention a relative wet strength of more than 10% can be achieved.