The momentum balance equation and the balance equation for the pressure tensor of a collision-free one-species magnetoplasma are linearized and Fourier-transformed, together with Maxwell's curl equations. They are combined in an algebraic dispersion system for the average perturbation velocity of the plasma particles. To do this a set of five fourth-order projectors is introduced, constructed with the aid of a commutative ‘ring product’ of two second-order projectors. It is shown that the trace-free part of the anisotropic perturbation pressure tensor, usually ignored for the sake of simplicity in such analyses, is of the same order of magnitude as the trace of this tensor. The vanishing determinant of the dispersion system is the dispersion equation of fifth degree in the square of the refractive index.