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We discover that Fe-Co alloys develop a series of ordered ground-state structures in addition to the known CsCl-type structure. This new set of structures is found from a combinatorial ground-state search of 1.5×1010 bcc-based structures. The energies of the searched bcc structures are constructed with the cluster expansion method from few first-principles calculations of ordered Fe-Co structures. The set of new ground-state structures is explained from the decay behavior of the cluster expansion coefficients which allows us to identify a simple geometric motif common to all structures. The appearance of these FeCo superstructures offers a broader view of the ordering reactions in bipartite-lattice based binary alloys.