The momentum balance equations and the balance equations for the pressure tensors of a collision-free multi-species magnetoplasma are linearized and Fourier-transformed, together with Maxwell's curl equations. They are combined in an algebraic dispersion system for the electric wave vector. The vanishing determinant of this system is the dispersion equation. It is of degree $2+3s$ in the square of the refractive index if $s$ is the number of different particle species.