Using a He3-He4 dilution refrigerator coupled with adiabatic demagnetization, Au198 has been polarized in a magnetized Fe foil at 5 mK. By measuring the directional distribution of the γ rays emitted following the 2--->2+ first-forbidden β decays to Hg198, the β dealignment parameters U2 and U4 have been determined. For the 0.96-MeV transition, we find U2=0.795+/-0.007 and U4=0.347+/-0.03. This implies that about 60% of the total decays carry off no angular momentum, about 39% carry off one unit of angular momentum, while 1% +/-1% carry off two units of angular momentum. For the 0.29-MeV transition, we find U2=1.047+/-0.054, implying that less than 1% of the decays carry off one or two units of angular momentum.