A treebank is an important language resource for supervised statistical parsers. The parser induces the grammatical properties of a language from this language resource and uses the model to parse unseen data automatically. Since developing such a resource is very time-consuming and tedious, one can take advantage of already extant resources by adapting them to a particular application. This reduces the amount of human effort required to develop a new language resource. In this paper, we introduce an algorithm to convert an HPSG-based treebank into its parallel dependency-based treebank. With this converter, we can automatically create a new language resource from an existing treebank developed based on a grammar formalism. Our proposed algorithm is able to create both projective and non-projective dependency trees.