  We present a measurement of the Hubble constant made using geometric distance
measurements to megamaser-hosting galaxies. We have applied an improved
approach for fitting maser data and obtained better distance estimates for four
galaxies previously published by the Megamaser Cosmology Project: UGC 3789, NGC
6264, NGC 6323, and NGC 5765b. Combining these updated distance measurements
with those for the maser galaxies CGCG 074-064 and NGC 4258, and assuming a
fixed velocity uncertainty of 250 km s$^{-1}$ associated with peculiar motions,
we constrain the Hubble constant to be $H_0 = 73.9 \pm 3.0$ km s$^{-1}$
Mpc$^{-1}$ independent of distance ladders and the cosmic microwave background.
This best value relies solely on maser-based distance and velocity
measurements, and it does not use any peculiar velocity corrections. Different
approaches for correcting peculiar velocities do not modify $H_0$ by more than
${\pm}1{\sigma}$, with the full range of best-fit Hubble constant values
spanning 71.8-76.9 km s$^{-1}$ Mpc$^{-1}$. We corroborate prior indications
that the local value of $H_0$ exceeds the early-Universe value, with a
confidence level varying from 95-99% for different treatments of the peculiar
velocities.
