  The $\eta-\eta^{\prime}$ mixture is discussed in the chiral bag model to
calculate the pseudoscalar octet-singlet mixing angle consistent with the
experimental data. The color anomaly is taken into account with the modified
boundary conditions, which shows the relation between the $\eta^{\prime}$ mass
and the gluon condensate inside the chiral bag. We show, however, that
$\eta-\eta^{\prime}$ mixing angle can follow the Cheshire Cat Principle, i.e.,
insensitivity to the bag radius.
