  In the paper properties of the discrete analogue $D_m(h\beta)$ of the
differential operator $\frac{d^{2m}}{dx^{2m}}-\frac{d^{2m-2}}{dx^{2m-2}}$ are
studied. It is known, that zeros of differential operator
$\frac{d^{2m}}{dx^{2m}}-\frac{d^{2m-2}}{dx^{2m-2}}$ are functions $e^x$,
$e^{-x}$ and $P_{2m-3}(x)$. It is proved that discrete analogue $D_m(h\beta)$
of this differential operator also have similar properties.
