  This paper studies the stability properties of a two dimensional relative
velocity scheme for the Navier-Stokes equations. This scheme inspired by the
cascaded scheme has the particularity to relax in a frame moving with a
velocity field function of space and time. Its stability is studied first in a
linear context then on the non linear test case of the Kelvin-Helmholtz
instability. The link with the choice of the moments is put in evidence. The
set of moments of the cascaded scheme improves the stability of the
d'Humi\`eres scheme for small viscosities. On the contrary, a relative velocity
scheme with the usual set of moments deteriorates the stability.
