Neutron polarization analysis has been carried out in order to clarify the magnetic structures of multiple order parameter f -electron system NdB 4 . We confirmed the non-collinear 'all-in all-out' structure (Γ 4 ) of the in-plane moment, which is in good agreement with our previous neutron powder diffraction study. We found that the magnetic moment along the c-axis m c showed diagonally antiferromagnetic structure (Γ 10 ), inconsistent with previously reported 'vortex' structure (Γ 2 ). The microscopic mixture of these two structures with q 0 =(0, 0, 0) appears in phase II and remains stable in phases III and IV, where an incommensurate modulation coexists. The unusual magnetic ordering is phenomenologically understood via Landau theory with the primary order parameter Γ 4 coupled with higher-order secondary order parameter Γ 10 . The magnetic moments were estimated to be 1.8 ± 0.2 and 0.2 ± 0.05µ B at T =7.5 K for Γ 4 and Γ 10 , respectively. We also found that a long-period incommensurate modulation of the q 1 =(0, 0, 1/2) antiferromagnetic structure of m c with the propagation q s1 =(0.14, 0.14, 0.1) and q s2 =(0.2, 0, 0.1) in phase III and IV, respectively. The amplitude of sinusoidal modulation was about m c = 1.0 ± 0.2µ B at T =1.5 K. The local (0, 0, 1/2) structure consists of in-plane ferromagnetic and out-of-plane antiferromagnetic coupling of m c , opposite to the coexisting Γ 10 . The m c of Γ 10 is significantly enhanced up to 0.6µ B at T =1.5 K, which is accompanied by the incommensurate modulations. The Landau phenomenological approach indicates the higer-order magnetic and/or multipole interactions based on pseudo-quartet f -electron state play important role. * metoki.naoto@jaea.go.jp It is becoming ever more apparent that the unusual magnetic properties in rare earth and actinide compounds come from the nature of f -electrons with multiple order parameters and their competing interactions. Multipole ordering has been successfully understood in some light rare-earth [1-5] and actinide [6] compounds with small f -electron number, in most cases n ≤ 2. The f -electron states and the corresponding excitation spectra under crystalline electric field (CEF) are relatively simple in comparison with heavy rare-earth which are often very complicated and difficult to determine experimentally [7-9]. In this paper, we focused on NdB 4 , a challenge for Nd 3+ with 4f 3 , having 4 I 9/2 ground state. NdB 4 exhibits successive magnetic transitions at T 0 = 17.2 K, T N1 = 7.0 K, and T N2 = 4.8 K[10]. Previous magnetic and thermodynamic studies revealed the paramagnetic phase I (T > T 0 ), phase II (T N1 < T < T 0 ), phase III (T N2 < T < T N1 ), and phase IV (T < T N2 ), where the specific heat shows two λ-type anomalies at T N1 and T 0 , and a first-order-like anomaly at T N2 . The system with half-integer J favors magnetic ordering to release the entropy of the Kramers degeneracy. The mechanism of the successive transitions in NdB 4 , especially the type of order parameters, has not been fully understood. The g...