  We analyze stability of the planar orientational structure in a nematic
liquid crystal (NLC) cell with planar anchoring conditions at both substrates.
Specifically, we study the instabilities of the ground state caused by surface
elasticity at large saddle-splay elastic constant, $K_{24}$. For relatively
small $K_{24}$ violating the Ericksen inequalities the theory predicts that the
critical fluctuation mode of the wavelength, $\lambda_c$, will render the
structure unstable when the thickness of the cell is below its critical value,
$d_c$. The parity of the critical mode changes as the twist-splay ratio
$K_2/K_1$ is passing through the unity. Further increase of $K_{24}$ beyond the
second threshold value, $4K_1K_2/(K_1+K_2)$, leads to the instability with
respect to the short wavelength fluctuations regardless of the cell thickness.
We compute the critical thickness and the critical wavelength as functions of
$K_{24}$, the twist-splay ratio and the azimuthal anchoring strength.
