Recently it turns out that simple-looking elliptical galaxies and lenticular galaxies are more complex and intriguing than expected. One of the most surprising and intriguing findings in extragalactic studies during the last two decades is a discovery that color distribution of the globular clusters in these galaxies is bimodal, suggesting that there are two subpopulations: blue and red globular clusters. We present a determination of the two-dimensional shape parameters of the blue and red globular cluster systems (GCSs) in a large number of bright elliptical galaxies and lenticular galaxies. The position angles of both and red GCSs show a correlation with those of the stellar light distribution, showing that the major axes of the GCSs are well aligned with those of their host galaxies. However, the shapes of the red GCSs show a tight correlation with the stellar light distribution as with the rotation property of their host galaxies, while the shapes of the blue GCSs do much less. These provide clear geometric evidence that the origins of the blue and red globular clusters are distinct and that these galaxies may have dual halos: a blue (metal-poor) halo and a red (metal-rich) halo. These two halos show significant differences in metallicity, structure, and kinematics, indicating that they are formed in two distinguishable ways. The red halos might have formed via dissipational processes with rotation, while the blue halos are through accretion.