  We investigate a mechanism to form and keep a planar spatial distribution of
satellite galaxies in the Milky Way (MW), which is called the satellite plane.
It has been pointed out that the {\Lambda}CDM cosmological model hardly
explains the existence of such a satellite plane, so it is regarded as one of
the serious problems in the current cosmology. We here focus on a rotation of
the gravitational potential of a host galaxy, i.e., so-called a figure
rotation, following the previous suggestion that this effect can induce the
tilt of a so-called tube orbit. Our calculation shows that a figure rotation of
a triaxial potential forms a stable orbital plane perpendicular to the
rotational axis of the potential. Thus, it is suggested that the MW's dark halo
is rotating with its axis being around the normal line of the satellite plane.
Additionally, we find that a small velocity dispersion of satellites is
required to keep the flatness of the planar structure, namely the standard
derivation of their velocities perpendicular to the satellite plane needs
smaller than their mean rotational velocity on the plane. Although not all the
MW's satellites satisfy this condition, some fraction of them called member
satellites, which are prominently on the plane, satisfy it. We suggest that
this picture explaining the observed satellite plane can be achieved by the
filamentary accretion of dark matter associated with the formation of the MW
and a group infall of member satellites along this cosmic filament.
