UNi 4 B exhibits unusual properties and, in particular, a unique antiferromagnetic arrangement involving only 2͞3 of the U sites. Based on the low temperature behavior of this compound, we propose that the remaining 1͞3 U sites are nonmagnetic due to the Kondo effect. We derive a model in which the coexistence of magnetic and nonmagnetic U sites is the consequence of the competition between frustration of the crystallographic structure and instability of the 5f moments. [S0031-9007(96)01866-2] PACS numbers: 75.10. -b, 75.30.Mb