We present a new dependency parsing algorithm based on the decomposition of large sentences into smaller units such as clauses and intraclausal coordinations. For the identification of these units, new methods combining machine learning techniques and heuristic rules were developed. The algorithm was evaluated on the Slovene dependency treebank text corpus. Compared to the MSTP parser, currently the most accurate for Slovene, parsing accuracy was improved by 1.27 percentage points, which equals 6.4 % relative error reduction.