  We have investigated magnetotransport properties and the topological
electronic structure of the half-Heusler compound TbPtBi. Our experiments
reveal an exceptionally large anomalous Hall effect (AHE) in the canted
antiferromagnetic state of TbPtBi with the anomalous Hall angle (AHA) reaching
~0.68-0.76, which is a few times larger than the previously reported record in
GdPtBi. First-principles electronic structure and the associated anomalous Hall
conductivity were computed in order to interpret the experimental results. Our
analysis shows that the AHE in TbPtBi does not originate from the Weyl points
but that it is driven by the large net Berry curvature produced by the
anticrossing of spin-split bands near the Fermi level in TbPtBi.
