  We demonstrate how to produce a stable multispeed lattice Boltzmann method
(LBM) for a wide range of velocity sets, many of which were previously thought
to be intrinsically unstable. We use non-Gauss--Hermitian cubatures. The method
operates stably for almost zero viscosity, has second-order accuracy,
suppresses typical spurious oscillation (only a modest Gibbs effect is present)
and introduces no artificial viscosity. There is almost no computational cost
for this innovation.
  DISCLAIMER: Additional tests and wide discussion of this preprint show that
the claimed property of coupled steps: no artificial dissipation and the
second-order accuracy of the method are valid only on sufficiently fine grids.
For coarse grids the higher-order terms destroy coupling of steps and
additional dissipation appears.
  The equations are true.
