  Dilution effects on the long-range ordered state of the doubly degenerate
$e_g$ orbital are investigated. Quenched impurities without the orbital degree
of freedom are introduced in the orbital model where the long-range order is
realized by the order-from-disorder mechanism. It is shown by the Monte-Carlo
simulation and the cluster-expansion method that a decrease in the orbital
ordering temperature by dilution is remarkable in comparison with that in the
randomly diluted spin models. Tiltings of orbitals around impurity cause this
unique dilution effects on the orbital systems. The present theory provides a
new view point for the recent experiments in KCu$_{1-x}$Zn$_x$F$_3$.
