We report the discovery of a new allotrope of iron by first principles calculations. This phase has Pmn2(1) symmetry, a six-atom unit cell (hence the name Fe6), and the highest magnetization density (Ms) among all the known crystalline phases of iron. Obtained from the structural optimizations of the Fe3C-cementite crystal upon carbon removal, Pmn2(1) Fe6 is shown to result from the stabilization of a ferromagnetic FCC phase, further strained along the Bain path. Although metastable from 0 to 50 GPa, the new phase is more stable at low pressures than the other well-known HCP and FCC allotropes and smoothly transforms into the FCC phase under compression. If stabilized to room temperature, for example, by interstitial impurities, Fe6 could become the basis material for high Ms rare-earth-free permament magnets and high-impact applications such as light-weight electric engine rotors or high-density recording media. The new phase could also be key to explaining the enigmatic high Ms of Fe16N2, which is currently attracting intense research activity.