Results are presented of calculations of the magnetic properties of U3Bi4 in the framework of the local density functional approximation (LDA). The calculations are carried out with a modified version of the augmented spherical wave (ASW) method that takes into account self-consistently the noncollinearity of the magnetization inside the atomic spheres and uses the full shape, instead of the spherically symmetric, intra-atomic potential. The new technique is discussed. The calculations for U3Bi4 are put into the larger context of the series of compounds U3X4 (X=P, As, Sb, Bi) which allows us to exhibit important trends in their magnetic properties. Thus we discuss in particular: the variation of the magnitude of the magnetic moment, the change of the direction of the magnetization axis and the regularities of the magnetocrystalline anisotropy in the series. We argue that U3Bi4, just as the other compounds in the series, belongs to the class of systems for which the noncollinearity of the magnetic structure is a necessary consequence of the symmetry of the system. The latter is analyzed and related to the results of the first-principles calculations of the complex magnetic structure in U3Bi4. We compare our results with other calculations and with available experimental data. (C) 2000 Elsevier Science S.A. All rights reserved.