  In recent years, it was found that there are several low/hard state of X-ray
binaries (XRBs) follow an `outliers' track of radio--X-ray correlation ($L_{\rm
R}\propto L_{\rm X}^{b}$ and $b\sim1.4$), which is much steeper than the former
universal track with $b\sim0.6$. In this work, we compile a sample of bright
radio-quiet active galactic nuclei (AGNs) and find that their hard X-ray photon
indices and Eddington ratios are positively correlated, which is similar to
that of `outliers' of XRBs, where both bright AGNs and `outliers' of XRBs have
bolometric Eddington ratios $\gtrsim1%L_{\rm Edd}$ ($L_{\rm Edd}$ is Eddington
luminosity). The Eddington-scaled radio--X-ray correlation of these AGNs is
also similar to that of `outliers' of XRBs, which has a form of $L_{\rm 5
GHz}/L_{\rm Edd}\propto (L_{\rm 2-10 keV}/L_{\rm Edd})^{c}$ with $c\simeq1.59$
and 1.53 for AGNs and XRBs respectively. Both the positively correlated X-ray
spectral evolution and the steeper radio--X-ray correlation can be regulated by
a radiatively efficient accretion flow (e.g., disk-corona). Based on these
similarities, we further present a new fundamental plane for `outliers' of XRBs
and bright AGNs in black-hole (BH) mass, radio and X-ray luminosity space:
$\log L_{\rm R}=1.59^{+0.28}_{-0.22} \log L_{\rm X}- 0.22^{+0.19}_{-0.20}\log
M_{\rm BH}-28.97^{+0.45}_{-0.45}$ with a scatter of $\sigma_{\rm R}=0.51\rm
dex$. This fundamental plane is suitable for radiatively efficient BH sources,
while the former plane proposed by Merloni et al. and Falcke et al. may be most
suitable for radiatively inefficient sources.
