A chunking algorithm with a Markov model is extended to accept bracketing constraints. The extended algorithm is implemented by modifying a state-of-the-art Japanese dependency parser. Then the effect of bracketing constraints in preventing parsing errors is evaluated. A method for improving the parser’s accuracy is proposed. That method adds brackets according to a set of optimal brackets obtained from a training corpus. Although the method’s coverage is limited, the F-measure for the sentences to which the method adds brackets is improved by about 7%.