  We have recently proposed a simple relativistic theory which reduces to
modified Newtonian dynamics for the weak-field quasistatic situations applied
to galaxies, and to cosmological behavior as in the $\Lambda$CDM model,
yielding a realistic cosmology in line with observations. A key requirement of
any such model is that Minkowski space is stable against linear perturbations.
We expand the theory action to second order in perturbations on a Minkowski
background and show that it leads to healthy dispersion relations involving
propagating massive modes in the vector and the scalar sector. We use
Hamiltonian methods to eliminate constraints present, demonstrate that the
massive modes have Hamiltonian bounded from below and show that a
nonpropagating mode with a linear time dependence may have unbounded
Hamiltonian for wave numbers $k< \mu$ and bounded otherwise. The scale $\mu$ is
estimated to be $\lesssim \mathrm{Mpc}^{-1}$ so that the low momenta
instability may only play a role on cosmological scales.
