A key question in the theory of high‐temperature superconductivity is whether off‐diagonal long‐range order can be induced wholly or in large part by repulsive electronic correlations. Electron pairs on cuprate and the iron‐based pnictide and chalcogenide alternant lattices may interact with a strong short‐range Coulomb repulsion and much weaker longer range attractive tail. Here, we show that such interacting electrons can cooperate to produce a superconducting state in which time‐reversed electron pairs effectively avoid the repulsive part but reside predominantly in the attractive region of the potential. The alternant lattice structure is a key feature of such a stabilization mechanism leading to the occurrence of high‐temperature superconductivity with or sign alternating s‐wave or s± condensate symmetries. © 2013 Wiley Periodicals, Inc.