Hexagonal UNi4B is magnetically frustrated, yet it orders antiferromagnetic
ally at T-N = 20 K. However, one-third of the U spins remains paramagnetic
below this temperature. In order to track these spins to lower temperature,
we measured the specific heat C of UNi4B between 100 mK and 2 K, in applie
d fields up to 9 T. A sharp kink in C at T* approximate to 330 mK is observ
ed at zero field, which we interpret as an indication of a second phase tra
nsition involving paramagnetic U. We attribute the rise in gamma = C/T betw
een 7 K and 330 mK and the absence of a large entropy liberated at T* to a
combination of Kondo screening effects and frustration that strongly modifi
es the low T transition.