A careful search for the ordering of Cu(1)OCu(1) monomers in a “herringbone” (HB) superstructure with the unit cell 2 2a 0 × 2b 0 × c 0 at x=0.32(2) and x=0.37(2) yielded negative results. The upper limit for the partial volume of this phase in a slowly cooled crystal with x=0.37(2) is estimated as 0.01%. A short-range ordering of chain fragments like in Ortho-II phase with an average chain length of three oxygen atoms is found instead while keeping the tetragonal symmetry. The HB superstructure is found in as-grown crystals with x∼0.20, but it has not been observed in slowly cooled crystals with x=0.23(3). Possible mechanisms of the HB phase formation are discussed.