  A theory with the action combining the Einstein--Hilbert term and graviton
mass terms violating Lorentz invariance is considered at linearized level about
Minkowskian background. It is shown that with one of the masses set equal to
zero, the theory has the following properties: (i) there is a gap of order $m$
in the spectrum, where $m$ is the graviton mass scale; (ii) the dispersion
relations at ${\bf p}^2 \gg m^2$ are $\omega^2 \propto {\bf p}^2$, the spectrum
of tensor modes being relativistic, while other modes having unconventional
maximum velocity; (iii) the VDVZ discontinuity is absent; (iv) the strong
coupling scale is $(mM_{Pl})^{1/2}$. The latter two properties are in sharp
contrast to the Lorentz-invariant gravity with the Pauli--Fierz mass term.
