The present invention is directed to a process comprising: (i) extracting ≧50% by weight of all carrageenan from a carrageenan-containing seaweed material to obtain a cellulose-containing seaweed residue; and (ii) purifying the cellulose-containing seaweed residue by at least one of hydrolysis or bleaching. The present invention is also directed to the cellulose obtained from the process, as well as products containing the cellulose-containing seaweed material.