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In this paper, we propose a new statistical Japanese dependency parser using a cascaded chunking model. Conventional Japanese statistical dependency parsers are mainly based on a probabilistic model, which is not always efficient or scalable. We propose a new method that is simple and efficient, since it parses a sentence deterministically only deciding whether the current segment modifies the segment on its immediate right hand side. Experiments using the Kyoto University Corpus show that the method outperforms previous systems as well as improves the parsing and training efficiency.