  We have analyzed 200 Rossi X-ray Timing Explorer observations of the black
hole candidate GX 339--4, all from the bright hard state periods between 1996
and 2005. Purpose of our study is to investigate the radiation mechanisms in
the hard state of GX 339--4. The broadband 3--200 keV spectra were successfully
modeled by a simple analytic model, power--law with an exponential cut-off
modified with a smeared edge. The obtained energy cut-off ($E_{\rm{cut}}$) was
distributed over 50--200 keV, and the photon index over 1.4--1.7. We found a
clear anti-correlation ($E_{\rm{cut}} \propto L^{-0.70\pm0.06}$) between the
X-ray luminosity ($L$) in 2--200 keV and $E_{\rm{cut}}$, when $L$ is larger
than $7 \times 10^{37}$ erg s$^{-1}$ (assuming a distance of 8 kpc), while
$E_{\rm{cut}}$ is roughly constant at around 200 keV when $L$ is smaller than
$7 \times 10^{37}$ erg s$^{-1}$. This anti-correlation remained unchanged by
adopting a more physical thermal Comptonization model, which resulted in the
anti-correlation that can be expressed as $kT_{\rm{e}} \propto
L^{-0.24\pm0.06}$. These anti-correlations can be quantitatively explained by a
picture in which the energy-flow rate from protons to electrons balances with
the inverse Compton cooling.
