We have commenced a 21-cm survey of the entire southern sky ( \delta < 0 ^ { \circ } , -1200 km s ^ { -1 } < v _ { \odot } < 12 , 700 km s ^ { -1 } ) which is “ blind ” , i.e . unbiased by previous optical information . In the present paper we report on the results of a pilot project which is based on data from this all-sky survey . The project was carried out on an area of 600 square degrees centred on the nearby Centaurus A ( Cen A ) group of galaxies at a mean velocity of v _ { \odot } \sim 500 km s ^ { -1 } . This was recently the subject of a separate and thorough optical survey . We found 10 new group members to add to 21 galaxies already known in the Cen A group : five of these are previously uncatalogued galaxies , while 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 _ { \odot } at the assumed group distance of 3.5 Mpc . The new detection with the largest H i mass is ESO174-G ? 001 with M _ { H { \sc i } } = 2.1 \times 10 ^ { 8 } M _ { \odot } . Prior to our survey this galaxy was an uncertain optical identification because of high galactic extinction . We found optical counterparts for all the H i detections , most of them intrinsically very faint ( M _ { B } < -13.0 ) low-surface brightness dwarf galaxies with H i profile line-widths suggestive of dynamics 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 i mass function , derived from all the known group galaxies in the interval 10 ^ { 7 } M _ { \odot } < M _ { H { \sc i } } < 10 ^ { 9 } M _ { \odot } , has a faint-end slope of 1.30 \pm 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 \pm 0.15 .