Several hole-doped BaFe₂As₂ compounds were recently shown to exhibit a second magnetic phase transition in the concentration range close to the full suppression of antiferromagnetic (AFM) order. At this additional transition ordered magnetic moments reorient from in-plane to out-of-plane alignment associated with a suppression of the orthorhombic distortion. We have studied the magnetic properties of such a representative hole-doped system, Ba_1–xNa_xFe₂As₂ with 0.25 ≤ x ≤ 0.40, by neutron diffraction on large single crystals. With increasing Na substitution (0.25 ≤ x ≤ 0.39) the AFM transition temperature sharply decreases, while the spin-reorientation transition temperature is rather constant, until both magnetic phases are completely suppressed at x = 0.40. For all studied Na concentrations the additional transition is related to the spin reorientation, which, however, is complete only in the middle of the concentration range of the out-of-plane phase. In the superconducting state, the intensities of magnetic Bragg reflections become heavily suppressed; this effect seems to increase for larger T_c and reaches ∼50% in Ba_0.61Na_0.39Fe₂As₂. In samples with coexisting in-plane and out-of-plane ordering, this superconductivity induced suppression of ordered moments is significantly stronger for the out-of-plane components indicating that this phase more strongly competes with superconductivity.