We have commenced a 21 cm survey of the entire southern sky (delta < 0 degr
ees, -1200 km s(-1) < v. < 12,700 km s(-1)) that is "blind," i.e., unbiased
by previous optical information. In the present paper we report on the res
ults of a pilot project that is based on data from this all-sky survey. The
project was carried out on an area of 600 deg(2) centered on the nearby Ce
ntaurus A (Cen A) group of galaxies at a mean velocity of v., similar to 50
0 km s(-1). This was recently the subject of a separate and thorough optica
l survey. We found 10 new group members to add to 21 galaxies already known
in the Cen A group: five of these are previously uncataloged galaxies, whi
le five were previously catalogued but not known to be associated with the
group. Most of the new members have H I masses close to our survey limit of
10(7) M . at the assumed group distance of 3.5 Mpc. The new detection with
the largest H I mass is ESO 174-G?001 with M-H I = 2.1 x 10(8) M .. Prior
to our survey this galaxy was an uncertain optical identification because o
f high Galactic extinction. We found optical counterparts for all the H I d
etections, most of them intrinsically very faint (M (B) > - 13.0), low surf
ace brightness dwarf galaxies with H I profile line-widths suggestive of dy
namics dominated by dark matter. The new group members add approximately 6%
to the H I mass of the group and 4% to its light. The H r mass function, d
erived from all the known group galaxies in the interval 10(7) M . <M-H I <
10(9) M . has a faint-end slope of 1.30 +/- 0.15, allowing us to rule out
a slope of 1.7 at 95% confidence. Even if the number in the lowest mass bin
is increased by 50%, the slope only increases to 1.45 +/- 0.15.