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We have commenced a 21-cm survey of the entire southern sky (\delta < 0degrees, -1200 km/s < v < 12700 km/s) which is ''blind'', i.e. unbiased byprevious optical information. In the present paper we report on the results ofa pilot project which is based on data from this all-sky survey. The projectwas carried out on an area of 600 square degrees centred on the nearbyCentaurus A (Cen A) group of galaxies at a mean velocity of v ~ 500 km/s. Thiswas recently the subject of a separate and thorough optical survey.  We found 10 new group members to add to the 21 galaxies already known in theCen A group: five of these are previously uncatalogued galaxies, while fivewere previously catalogued but not known to be associated with the group.  We found optical counterparts for all the HI detections, most of themintrinsically very faint low surface brightness dwarfs. The new group membersadd approximately 6% to the HI mass of the group and 4% to its light. The HImass function, derived from all the known group galaxies in the interval 10^7\Msun of HI to 10^9 \Msun of HI, 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 inthe lowest mass bin is increased by 50%, the slope only increases to 1.45 +/-0.15.Comment: 19 pages Latex, 6 figures (Fig. 2 in four parts, Fig.5 in two parts).  To appear in The Astrophysical Journal (Vol. 524, October 1999

New Galaxies Discovered in the First Blind HiSurvey of the Centaurus A Group