We present 474 new proper motion stellar systems (500 objects) in the southern sky having no previously known components, with 0.40"/yr>{mu}>=0.18"/yr between declinations -47{deg} and 0{deg}. In this second paper utilizing the U.S. Naval Observatory third CCD Astrograph Catalog (UCAC3) we complete our sweep of the southern sky for objects in the proper motion range targeted by this survey with R magnitudes ranging from 9.80 to 19.61. The new systems contribute a ~16% increase in the number of new stellar systems for the same region of sky reported in previous SuperCOSMOS Research Consortium On Nearby Stars (RECONS) surveys. Among the newly discovered stellar systems are 16 multiples, plus an additional ten components that are new common proper motion companions to previously known objects. A comparison of UCAC3 proper motions to those from Hipparcos, Tycho-2, Southern Proper Motion, and SuperCOSMOS indicates that all proper motions are consistent to ~10mas/yr, with the exception of SuperCOSMOS. Distance estimates are derived for all stellar systems having SuperCOSMOS Sky Survey B_J_, R_59F_, and I_IVN_ plate magnitudes and Two Micron All Sky Survey (2MASS) infrared photometry. We find five new red dwarf systems estimated to be within 25pc. These discoveries support results from previous proper motion surveys suggesting that more nearby stellar systems are to be found, particularly in the fainter, slower moving samples. In this second paper utilizing the UCAC3 we complete our sweep of the southern sky for objects in the proper motion range targeted by this survey with R magnitudes ranging from 9.80 to 19.61.