  The self-consistent field approach for the electric dipolar ultracold
spin-1/2 fermions is discussed. Contribution of the exchange part of the
electric dipole interaction is found. Hence we obtain a model of dipolar
fermions beyond the self-consistent field approximation. It is shown that the
exchange interaction of electric dipolar fermions depends on the
spin-polarisation of the system. For instance the electric dipole exchange
interaction equals to zero for spin-unpolarised systems, namely all low laying
quantum states occupied by two-particles with opposite spins. In opposite limit
of the full spin polarisation of the degenerate fermions, then we have one
particle in each quantum states, the exchange interaction has maximum value,
which is comparable with the self-consistent field part of the dipole-dipole
interaction. The self-consistent part of the electric dipole-dipole interaction
gives a positive contribution into the spectrum of collective excitations,
while the exchange part of the dipole-dipole interaction leads to a negative
term in the spectrum. At angles between the equilibrium polarisation and the
direction of wave propagation close to $\pi/2$ the full dipolar part of the
spectrum becomes negative. At the electric dipole moment of fermions of order
of several Debay the dipolar part is large enough to exceed the Fermi pressure,
that reveals in an instability.
