  We report the first results of a long term program aiming to provide accurate
independent estimates of the Hubble constant (H0) using the L-sigma distance
estimator for Giant extragalactic HII regions (GEHR) and HII galaxies.
  We have used VLT and Subaru high dispersion spectroscopic observations of a
local sample of HII galaxies, identified in the SDSS DR7 catalogue in order to
re-define and improve the L(Hbeta)-sigma distance indicator and to determine
the Hubble constant. To this end we utilized as local calibration or `anchor'
of this correlation, GEHR in nearby galaxies which have accurate distance
measurements determined via primary indicators. Using our best sample of 69
nearby HII galaxies and 23 GEHR in 9 galaxies we obtain H0=74.3 +- 3.1
(statistical) +- 2.9 (systematic) km /s Mpc, in excellent agreement with, and
independently confirming, the most recent SNe Ia based results.
