- Geometrical symmetries are commonly exploited to improve the efficiency of search algorithms. We introduce a new logical symmetry in permutation state spaces which we call duality. We show that each state has a dual state. Both states share important attributes and these properties can be used to improve search efficiency. We also present a new search algorithm, dual search, which switches between the original state and the dual state when it seems likely that the switch will improve the chances of a cutoff. The decision of when to switch is very important and several policies for doing this are investigated. Experimental results show significant improvements for a number of applications.