  We investigate the origin of the orbital ordering in the paramagnetic phase
of KCrF$_3$. All previous studies described structural parameters of the
paramagnetic phase using a magnetic ordering in the compound. Our simulations
of real paramagnetic KCrF$_3$ were performed within an approach combining
density functional theory and dynamical mean field theory (DFT+DMFT). As a
result, it was found that the experimentally observed cooperative Jahn-Teller
effect is successfully described in a lattice relaxation calculation for
structure without any long-range magnetic ordering. It is established that the
existence of the orbital ordering even in undistorted perovskite structure
clearly confirms the electronic origin of the orbital ordering in KCrF$_3$.
