We introduce a new approach to transitionbased dependency parsing in which the parser does not directly construct a dependency structure, but rather an undirected graph, which is then converted into a directed dependency tree in a post-processing step. This alleviates error propagation, since undirected parsers do not need to observe the single-head constraint. Undirected parsers can be obtained by simplifying existing transition-based parsers satisfying certain conditions. We apply this approach to obtain undirected variants of the planar and 2-planar parsers and of Covington’s non-projective parser. .