We present here for the first time observations of the inverse correlation between the ion temperature anisotropy and plasma beta in the Earth's high-latitude magnetosheath. Hot proton data with energies of 0.3--8 keV were obtained from magnetosheath passages by the Hawkeye spacecraft which had a polar orbit with an apogee of 20--21 RE. A newly developed technique has been used to calculate the distribution functions of protons in their non-streaming frame in which their first-order anisotropy is absent. The ion-energy dependence of distribution functions indicates the existence of two hot ion components. Thus the correlation has been examined for each hot ion component separately. We have analyzed three Hawkeye magnetosheath passes during which the magnetosheath's magnetic field was close to the spacecraft spin plane, so that the two-dimensional Hawkeye sensor can adequately sample temperature anisotropies. Results of our analyses are consistent with the theoretical prediction given by Gary et al. [1994; 1995> that a universal inverse-correlation relationship exists between the temperature anisotropy and plasma beta of hot ions. ¿ 1998 American Geophysical Union