  We have checked the existence of a zone of avoidance oriented along the
Galactic rotation axis in the globular cluster (GC) system of the Galaxy and
performed a parametrization of this zone in the axisymmetric approximation. We
show that an unambiguous conclusion about the existence of an axial zone of
avoidance and its parameters cannot be reached based on the maximization of the
formal cone of avoidance due to the discreteness of the GC system. The
ambiguity allows the construction of the representation of voids in the GC
system by a set of largest-radius meridional cylindrical voids to be overcome.
As a result of our study, we have managed to identify northern and southern
axial zones of avoidance with similar characteristics. The combined zone of
avoidance is traceable at $|Z| \gtrsim 1$ kpc and is similar in shape to a
double cone whose axis crosses the region of greatest GC number density. By
modeling the distribution of Galactocentric latitudes for GCs, we have
determined the half-angle of the cone of avoidance ${\alpha}_0 =
15.0^{+2.1}_{-4.1}$ deg and the distance to the Galactic center $R_0 = 7.3 \pm
0.5$ kpc (in the scale of the Harris (1996) catalog, the 2010 version) as the
distance from the Sun to the point of intersection of the cone axis with the
center--anticenter line. A correction to the calibration obtained from Galactic
objects only leads to an estimate of $R_0 = 7.2 \pm 0.5|_{stat} \pm
0.3|_{calib}$ kpc. The probability that the zone of avoidance at the
characteristics found is random in nature is $\le 2\%$. We have revealed
evidence for the elongation of the zone of avoidance in the direction
orthogonal to the center--anticenter axis, which, just as the north--south
difference in this zone, may be attributable to the influence of the Magellanic
Clouds. The detectability of similar zones of avoidance in the GC systems of
external galaxies is discussed.
