  Magnetic and orbital structures in KCuF$_{3}$ are revisited by the cluster
self-consistent field approach developed recently. We clearly showed that due
to the inherent frustration, the ground state of the system with the
superexchange and Jahn-Teller phonon-mediated orbital couplings is highly
degenerate without broken symmetry; the orthorhombic crystalline field
splitting arising from static Jahn-Teller distortion stabilizes the orbital
ordering, about 42% in the $x^{2}-y^{2}$ orbit and 58% in the $3z^{2}-r^{2}$
orbit in sublattices. The magnetic moment of Cu is considerably reduced to
0.49$\mu_{B}$, and the magnetic coupling strengths are highly anisotropic,
J$_{c}$/J$_{ab}$ $\approx$ 26. These results are in agreement with the
experiments, implying that as an orbital selector, the crystalline field plays
an essential role in stabilizing the ground state of KCuF$_{3}$. The 1s-3d
resonant X-ray scattering amplitudes in KCuF$_{3}$ with the {\it type-a} and
{\it type-d} structures are also presented.
