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The orbital distribution of the S-star cluster surrounding the supermassiveblack hole in the center of the Milky Way is analyzed. A tight, roughlyexponential dependence of the pericenter distance r$_{p}$ on orbitaleccentricity e$_{\star}$ is found, $\log ($r$_p)\sim$(1-e$_{\star}$), whichcannot be explained simply by a random distribution of semi-major axes andeccentricities. No stars are found in the region with high e$_{\star}$ andlarge log r$_{p}$ or in the region with low e$_{\star}$ and small log r$_{p}$.G-clouds follow the same correlation. The likelihood P(logr$_p$,(1-e$_{\star}$)) to determine the orbital parameters of S-stars isdetermined. P is very small for stars with large e$_{\star}$ and large logr$_{p}$. S-stars might exist in this region. To determine their orbitalparameters, one however needs observations over a longer time period. On theother hand, if stars would exist in the region of low log r$_{p}$ and smalle$_{\star}$, their orbital parameters should by now have been determined. Thatthis region is unpopulated therefore indicates that no S-stars exist with theseorbital characteristics, providing constraints for their formation. We callthis region, defined by $\log$ (r$_p$/AU) $<$ 1.57+2.6(1-e$_{\star})$, the zoneof avoidance. Finally, it is shown that the observed frequency ofeccentricities and pericenter distances is consistent with a random sampling oflog r$_{p}$ and e$_{\star}$. However, only if one takes into account that nostars exist in the zone of avoidance and that orbital parameters cannot yet bedetermined for stars with large r$_{p}$ and large e$_{\star}$.

The Orbital Structure and Selection Effects of the Galactic Center S-Star Cluster