  We report on the ESR, magnetization and magnetic susceptibility measurements
performed over a large temperature range, from 1.5 to 750 K, on high-quality
stoichiometric LiNiO2. We find that this compound displays two distinct
temperature regions where its magnetic behavior is anomalous. With the help of
a statistical model based on the Kugel'-Khomskii Hamiltonian, we show that
below T_of ~ 400 K, an orbitally-frustrated state characteristic of the
triangular lattice is established. This then gives a solution to the
long-standing controversial problem of the magnetic behavior in LiNiO2.
