We explore X-ray spectral evolution and radio–X-ray correlation simultaneously for four X-ray binaries (XRBs). We find that hard X-ray photon indices, Γ, are anti- and positively correlated to X-ray fluxes when the X-ray flux, F3–9keV, is below and above a critical flux, FX,crit, which may be regulated by ADAF and disk-corona respectively. We find that the data points with anti-correlation of Γ-F3–9keV follow the universal radio–X-ray correlation of FR ∝ FXb (b ~ 0.5-0.7), while the data points with positive X-ray spectral evolution follow a steeper radio–X-ray correlation (b ~ 1.4, the so-called ‘outliers track’). The bright active galactic nuclei (AGNs) share similar X-ray spectral evolution and radio–X-ray correlation as XRBs in ‘outliers’ track, and we present a new fundamental plane of log LR=1.59+0.28−0.22 log LX−0.22+0.19−0.20 log MBH−28.97+0.45−0.45 for these radiatively efficient BH sources.