In the external field slightly inclined to the x-or y-axis of the frustrated tetragonal antiferromagnet Pr 2 CuO 4 , a transition is discovered from the phase with orthogonal antiferromagnetic spin subsystems along [1,0,0] and [0,1,0] to the phase with the collinear spins. This phase is shown to be due to the pseudodipolar interaction, and transforms into the spin-flop phase (S⊥H) asymptotically at very high field. The discovered phase transition holds at T = 0 and is a quantum one, with the transition field being the critical point and the angle between two subsystems being the order parameter. Rare-earth cuprates R 2 CuO 4 (R = Pr, Nd, Sm, Eu, Gd), which originally had drown attention as parent compounds for the electron-doped high-T C superconductors, now are being extensively studied as two-dimensional quantum Heisenberg antiferromagnets. These materials have a tetragonal structure with the space group I4/mmm. The CuO 2 planes give a motif of the structure, with the Cu 2+ ions being coordinated by regular squares of oxygen neighbours [1]. A very important feature of this tetragonal body-centred structure is a shift of adjacent CuO 2 planes by [1/2,1/2,1/2]. Due to very strong in-plane superexchange interaction, J = 124(3) meV [2], each Cu 2+ ion (S = 1/2) has four nearest neighbors with the opposite spins. Therefore, the mean field, produced on each copper ion by the adjacent plains is cancelled. In the absence of exchange field, the interplanar spin orientation should be very sensitive to any weak interaction that violates the symmetry. Shender [3] has shown that in a similar situation of the bcc lattice the quantum zero-point spin fluctuations stabilize a collinear orientation of the spin subsystems, which has been confirmed experimentally [4].For interpretation of the early neutron diffraction data a collinear model was used with the spins along [1,1,0] and with a propagation vector k 1 = (π/a) [1,1,0] in the same direction [5,6]. Certainly there should be another domain with the spins along [1,−1,0] and with k 2 = (π/a) [1,−1,0]. A different model with two vectors, k 1 and k 2 (2-k structure) that results in exactly the same intensities of the magnetic reflections has been also proposed [6]. In this model two antiferromagnetic subsystems are orthogonal, with the spins in positions (0,0,0) and (1/2,1/2,1/2) along [1,0,0] and [0,−1,0] directions, respectively, as shown in Fig. 1(a). Neutron diffraction experiments in the external magnetic field applied in the [1,1,0] direction [7][8][9][10][11] have definitely proved that the copper spin subsystems are orthogonal in spite of the quan-