  We analyze in this paper the existence of the "out-of-plane" equilibrium
points in the restricted three-body problem with oblateness. From the series
expansion of the potential function of an oblate asteroid, we show analytically
all equilibrium points locate on the orbital plane of primaries and how
artificial equilibrium points may arise due to an inappropriate application of
the potential function. Using the closed form of the potential of a triaxial
ellipsoid, we analytically demonstrate that the gravitational acceleration in
$z$-direction is always pointing toward the equatorial plane, thus it could not
be balanced out at any value of $z\neq 0$ and the out-of-plane equilibrium
points cannot exist. The out-of-plane equilibrium points appear only when
additional acceleration other than the gravitation from primaries is taken into
account. We suggest that special attention must be paid to the application of
the spherical harmonics expansion of potential to find the equilibrium points,
especially when these points may be very close to the celestial body.
