We have studied the magnetic ordering in Ba1-xNaxFe2As2 with 0.25 ⩽ x ⩽ 0.4 by unpolarized and polarized neutron diffraction using single crystals. Unlike most FeAs-based compounds that magnetically order, Na-doped BaFe2As2 exhibits two successive magnetic transitions: For x = 0.35, upon cooling, magnetic order occurs at ∼ 70 K with in-plane magnetic moments being arranged as in pure or Ni-, Co-, or K-doped BaFe2As2 samples. At a temperature of ∼ 46 K a second phase transition occurs, which the single-crystal neutron-diffraction experiments can unambiguously identify as a spin reorientation. At low temperatures, the ordered magnetic moments in Ba065Na0.35Fe2As2 point along the c direction. The two nearly degenerate magnetic states document orbital degeneracy to persist in the superconducting phase. [ABSTRACT FROM AUTHOR]