Herein, we present the process of developing the first Hungarian Dependency TreeBank. First, short references are made to dependency grammars we considered important in the development of our Treebank. Second, mention is made of existing dependency corpora for other languages. Third, we present the steps of converting the Szeged Treebank into dependency-tree format: from the originally phrase-structured treebank, we produced dependency trees by automatic conversion, checked and corrected them thereby creating the first manually annotated dependency corpus for Hungarian. We also go into detail about the two major sets of problems, i.e. coordination and predicative nouns and adjectives. Fourth, we give statistics on the treebank: by now, we have completed the annotation of business news, newspaper articles, legal texts and texts in informatics, at the same time, we are planning to convert the entire corpus into dependency tree format. Finally, we give some hints on the applicability of the system: the present database may be utilized ― among others ― in information extraction and machine translation as well.