Planar tetracoordinate fluorine (ptF) species are very exotic and scarce due to high electronegativity of fluorine. Herein we report the ternary square ptF cluster, D4h FK4H4-, which is composed of a F center, a square K4 ring, and four outer H bridges. It is a true global minimum (GM) structure and possesses good dynamic stability. Bonding analyses indicate that there are four lone pairs for the central F atom, along with four K-H-K three-center two-electron (3c-2e) σ bonds for the peripheral K4H4 ligand ring. The stability of ptF is dominated by multicenter ionic bonds rather than the supposed σ aromaticity of the system. Excitingly, it is a pseudohalogen anion with the VDE 3.57 eV at the CCSD(T) level. The merge of ptF with pseudohalogen anion character makes the FK4H4- cluster an exotic species, which will motivate theoretical and experimental studies on novel ptF species as well as superhalogens.