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A Robinson-Foulds (RF) supertree for a collection of input trees is a tree containing all the species in the input trees that is at minimum total RF distance to the input trees. Thus, an RF supertree is consistent with the maximum number of splits in the input trees. Constructing RF supertrees for rooted and unrooted data is NP-hard. Nevertheless, effective local search heuristics have been developed for the restricted case where the input trees and the supertree are rooted. We describe new heuristics, based on the Edge Contract and Refine (ECR) operation, that remove this restriction, thereby expanding the utility of RF supertrees. Our experimental results on simulated and empirical data sets show that our unrooted local search algorithms yield better supertrees than those obtained from MRP and rooted RF heuristics in terms of total RF distance to the input trees and, for simulated data, in terms of RF distance to the true tree.