We present a novel transition system, based on the Covington non-projective parser, introducing non-local transitions that can directly create arcs involving nodes to the left of the current focus positions. This avoids the need for long sequences of No-Arc transitions to create long-distance arcs, thus alleviating error propagation. The resulting parser outperforms the original version and achieves the best accuracy on the Stanford Dependencies conversion of the Penn Treebank among greedy transition-based algorithms.