Exact inference in high-order graph-based non-porjective dependency parsing is intractable. Hence, sophisticated approximation techniques based on algorithms such as belief propagation and dual decomposition have been employed. In contrast, we propose a simple greedy search approximation for this problem which is very intuitive and easy to implement. We implement the algorithm within the second-order TurboParser and experiment with the datasets of the CoNLL 2006 and 2007 shared task on multilingual dependency parsing. Our algorithm improves the run time of the parser by a factor of 1.43 while losing 1% in UAS on average across languages. Moreover, an ensemble method exploiting the joint power of the parsers, achieves an average UAS 0.27% higher than the TurboParser.