Sulfated galactan kappa-carrageenan is a linear polysaccharide with a repeating disaccharide sequence of alternating 4-sulfated 3-linked galactose and 4-linked 3,6-anhydrogalactose units. In contrast to many examples of chemical hydrolysis of polysaccharides, mild acid treatment of kappa-carrageenan resulted in facile and highly specific cleavage. In this article, we report the identification, by various MS and chromatographic techniques, of an unexpected series of exclusively odd-numbered oligosaccharide fragments from its hydrolytic products. Detailed sequence analysis of the products indicated that all the oligosaccharide fragments have the 4-sulfated 3-linked galactose residues at both the reducing and the nonreducing ends. Further detailed investigation and analysis suggested that these odd-numbered oligosaccharides were derived from two-step cleavages of the glycosidic bonds on either sides of the 3,6-anhydrogalactose residues. Neutral galactan agarose also contains 3,6-anhydrogalactose and has a similar backbone sequence, and exhibited similar results upon mild acid hydrolysis. It is highly unusual to obtain exclusively odd-numbered oligosaccharides from polysaccharides composed of ordered disaccharide repeats.