We investigate the magnetic phase transition in UNi4B by specific heat
, c(T), thermal expansion and resistivity under pressure. These experi
ments reveal that the hexagonal symmetry is not broken at T-N = 20 K,
and predicts a hydrostatic pressure dependence of T-N of - 29 mK/kbar,
close to the result from resistivity. The anomalous upturn of c/T to
470 mJ/mol K-2 at 0.4 K is reduced to 160 mJ/mol K-2 in 16T parallel t
o b-axis. The specific heat critical exponent alpha = - 0.15(2) sugges
ts 3D Heisenberg universality in zero field.