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Several superconducting transition temperatures in the range of 30-46 K were reported in the recently discovered intercalated FeSe system (A1-xFe2-ySe2, A = K, Rb, Cs, Tl). Although the superconducting phases were not yet conclusively decided, more than one magnetic phase with particular orders of iron vacancy and/or potassium vacancy were identified, and some were argued to be the parent phase. Here we show the discovery of the presence and ordering of iron vacancy in nonintercalated FeSe (PbO-type tetragonal β-Fe1-xSe). Three types of iron-vacancy order were found through analytical electron microscopy, and one was identified to be nonsuperconducting and magnetic at low temperature. This discovery suggests that the rich-phases found in A1-xFe2-ySe2 are not exclusive in Fe-Se and related superconductors. In addition, the magnetic β-Fe1-xSe phases with particular iron-vacancy orders are more likely to be the parent phase of the FeSe superconducting system instead of the previously assigned β-Fe1+δTe.