  We study quadric surfaces in the 3-dimensional Euclidean space which are of
coordinate finite type Gauss map with respect to the second fundamental form
$II$, i.e., their Gauss map vector $\boldsymbol{n}$ satisfies the relation
$\Delta ^{II}\boldsymbol{n}=\varLambda \boldsymbol{n}$, where $\Delta ^{II}$
denotes the Laplace operator of the second fundamental form $II$ of the surface
and $\varLambda$ is a square matrix of order 3. We show that helicoids and
spheres are the only class of surfaces mentioned above satisfying $\Delta
^{II}\boldsymbol{n}=\varLambda \boldsymbol{n}$.
