  A Landau fluid model for a collisionless electron-proton magnetized plasma,
that accurately reproduces the dispersion relation and the Landau damping rate
of all the magnetohydrodynamic waves, is presented. It is obtained by an
accurate closure of the hydrodynamic hierarchy at the level of the fourth order
moments, based on linear kinetic theory. It retains non-gyrotropic corrections
to the pressure and heat flux tensors up to the second order in the ratio
between the considered frequencies and the ion cyclotron frequency.
