We report our analysis of the properties of galaxy clustering for a new redshift sample of galaxies, the CfA2- South catalog, using statistical methods that do not rely on the assumption of homogeneity. We find that, up to ~20 h~(-1) Mpc, which is the largest scale to which correlation properties can be reliably inferred, the galaxy clustering is scale invariant and characterized by a fractal dimension D = 1.9 ± 0.1. Further, there is no statistical evidence for homogeneity at any of the larger scales (up to ～150 h~(-1) Mpc) probed more weakly by the caialog. These results mean that characteristic "correlation lengths" for the clustering of galaxies derived using standard methods of analysis are not meaningful. Further, the results are very consistent with those obtained from many other catalogs using the methods adopted here, which show the D ≈ 2 fractal continuing to beyond 100 h~(-1) Mpc. The incompleteness of the relevant data conjectured by various authors to give rise to such behavior is therefore proved to have no significant effect (up to 20 h~(-1) Mpc) on the measured correlations.