``A novel polymer having 1,3-cyclobutanedione unit in the main chain was prepared by cycloaddition polymerization of the bisketene derived from 1,4-cyclohexanedicarbonyl chloride. The polymer was soluble in MEOH, acetone, and CHCl3. The structure of the polymer was confirmed by TR, H-1-, and C-13-NMR spectroscopies compared with those of the model compounds. The polymer was found to contain anhydride band as well as 1,3-cyclobutanedione unit in the main chain. The anhydride bond in the polymer was cleaved by MeOH under reflux condition in benzene.