We have completed a 21-cm survey of a 600 square degree region of the Centaurus A group of galaxies at a redshift of 500 km as part of a larger survey of the entire southern sky. This group of galaxies was recently the subject of a separate and thorough optical survey (CÓÄtÓ? et al. 1997), and thus presented an ideal comparison for us to test the survey performance. We have identified 10 new group members to add to the 21 already known in our survey area. Six of the new members are previously uncatalogued galaxies, while four were catalogued but assumed not to be group members. Including the 7 known members outside of our survey area, this brings the total known number of Cen A members to 38. All of the new HI detections have optical counterparts, most being intrinsically very faint (M_B > -13.0), late-type low surface brightness dwarfs. Most of the new members have HI masses only a few times our survey limit of 10⁷ M at an assumed distance for the group of 3.5 Mpc, and are extremely gas-rich, with a median M_HI/L_B > 1. Our limiting HI sensitivity was actually slightly worse than the HI follow-up observations of the CÓÄtÓ? et al. optical survey, yet we have already increased the known number of group members by 50% using an HI survey technique. While we have increased the known number of members by 50%, these new members contribute <4% to its light.