We propose a method for improving the dependency parsing of complex sentences. This method assumes segmentation of input sentences into clauses and does not require to re-train a parser of one's choice. We represent a sentence clause structure using clause charts that provide a layer of embedding for each clause in the sentence. Then we formulate a parsing strategy as a two-stage process where (i) coordinaed and subordinated clauses of the sentence are parsed separately with respect to the sentence clause chart and (ii) their dependency trees become subtrees of the final tree of the sentence. The object language is Czech and the parser used is a maximum spanning tree parser trained on the Prague Dependency Treebank. We have achieved an average 0.97% improvement in the unlabeled attachment score.