We determined the f odd,Ba values, 0.46 ± 0.08, 0.51 ± 0.09, 0.50 ± 0.13, 0.48 ± 0.12, which correspond to the rcontribution 100% for four r-II stars, CS 29491-069, HE 1219-0312, HE 2327-5642 and HE 2252-4225, respectively. Our results suggest that almost all of the heavy elements (in the range from Ba to Pb) in r-II stars have a common origin, that is, from a single r-process (the main r-process). We found that the f odd,Ba has a intrinsic nature, and should keep constant value of about 0.46 in the main r-process yields, which is responsible for the heavy element enhancement of r-II stars and of our Galaxy chemical enhancement. In addition, except the abundance ratio [Ba/Eu] the f odd,Ba is also an important indicator, which can be used to study the relative contributions of the r-and s-process during the chemical evolution history of the Milky Way and the enhancement mechanism in stars with peculiar abundance of heavy elements.