  The relation between the central mass and quasar luminosity (M_BH \propto
L^{\alpha}FHWM^2) links a given Eddington ratio with a value of H_0, within a
cosmology with fixed (\Omega_m,\Omega_{\Lambda}). We point out that because the
relation is calibrated at low z using distance independent reverberation
mapping to get the BLR size, the derived M_BH interestingly does not depend on
H_0, while L/L_Edd is sensitive to H_0, but rather robust to changes of
\Omega_{\Lambda} in the standard flat model. This means, e.g., that enough of
extragalactic objects radiating at the Eddington limit could be used to study
the global Hubble constant in a new way, bypassing the local distance ladder.
The method could become practical when systematic errors in derived M_BH are
understood and objects with L /leq L_Edd can be independently identified. As an
illustration, if we take a sample of tranquil very luminous quasars in the
redshift range 0.5 < z < 1.6, and assume that they are radiating with L_bol
\leq L_Edd, then the usual numeric factors used for calculating M_BH and L_bol
would lead to the result that the Hubble constant must be larger than 45
km/s/Mpc.
