(2-->5)-1,4-Anhydro-3-O-methyl-pentitol, which is a novel carbohydrate polymer without an anomeric linkage, was synthesized by cationic cyclopolymerization of 1,2: 4,5-dianhydro-3-O-methylxylitol. When BF3 . OEt2 was used as the initiator, soluble polymers were obtained in 28 to 50% yield. These polymers have number-average molecular weights of 1150 to 2340 corresponding to an average degree of polymerization of 8.8 to 18.0. It was confirmed by C-13 NMR that the resulting polymer mainly consists of 1,4-anhydro-3-O-methyl-DL-arabinitol units.