  We consider tangent cones to Schubert subvarieties of the flag variety $G/B$,
where $B$ is a Borel subgroup of a reductive complex algebraic group $G$ of
type $E_6$, $E_7$ or $E_8$. We prove that if $w_1$ and $w_2$ form a good pair
of involutions in the Weyl group $W$ of $G$ then the tangent cones $C_{w_1}$
and $C_{w_2}$ to the corresponding Schubert subvarieties of $G/B$ do not
coincide as subschemes of the tangent space to $G/B$ at the neutral point.
