The relationship between the integrated H β line luminosity and the velocity dispersion of the ionized gas of H II galaxies and giant H II regions represents an exciting standard candle that presently can be used up to redshifts z ∼ 4. Locally it is used to obtain precise measurements of the Hubble constant by combining the slope of the relation obtained from nearby (z ≤ 0.2) H II galaxies with the zero-point determined from giant H II regions belonging to an ‘anchor sample’ of galaxies for which accurate redshift-independent distance moduli are available. We present new data for 36 giant H II regions in 13 galaxies of the anchor sample that includes the megamaser galaxy NGC 4258. Our data are the result of the first 4 yr of observation of our primary sample of 130 giant H II regions in 73 galaxies with Cepheid determined distances. Our best estimate of the Hubble parameter is 71.0 ± 2.8(random) ± 2.1(systematic) km s^{− 1}Mpc^{− 1}. This result is the product of an independent approach and, although at present less precise than the latest SNIa results, it is amenable to substantial improvement.