  Recently a correlation between the radio and X-ray luminosities is found,
$L_{\rm R}\propto L_{\rm X}^{0.7}$, in black hole sources including black hole
candidates in our galaxy and active galactic nuclei. We first show that the
correlation can be understood in the context of an accretion-jet model
developed for explaining the spectral and timing properties of XTE J1118+480.
More importantly, we show that when the X-ray luminosity is below a critical
value, $\la (10^{-5}$--$10^{-6}) L_{\rm Edd}$, if the jet persists, the
correlation should turn and become steeper, $L_{\rm R}\propto L_{\rm
X}^{1.23}$, and the X-ray radiation of the system should be dominated by the
emission from the jet, rather than by the accretion flow. Possible
observational evidence for our predictions is presented and future observations
to further test our predictions are proposed.
