  We use the HI-selected galaxy sample from the Arecibo Dual-Beam Survey
(Rosenberg & Schneider 2000) to determine the shape of the HI mass function of
galaxies in the local universe using both the step-wise maximum likelihood and
the 1/V_tot methods. Our survey region spanned all 24 hours of right ascension
at selected declinations between 8 and 29 degrees covering ~430 deg^2 of sky in
the main beam. The survey is not as deep as some previous Arecibo surveys, but
it has a larger total search volume and samples a much larger area of the sky.
We conducted extensive tests on all aspects of the galaxy detection process,
allowing us to empirically correct for our sensitivity limits, unlike the
previous surveys. The mass function for the entire sample is quite steep, with
a power-law slope of \alpha ~ -1.5. We find indications that the slope of the
HI mass function is flatter near the Virgo cluster, suggesting that
evolutionary effects in high density environments may alter the shape of the HI
mass function. These evolutionary effects may help to explain differences in
the HI mass function derived by different groups. We are sensitive to the most
massive sources (log M > 5x10^10 M\solar) over most of the declination range,
\~1 sr, and do not detect any massive low surface brightness galaxies. These
statistics restrict the population of Malin 1-like galaxies to <5.5x10^-6
Mpc^-3.
