  In this paper the constitutive relations for moving media with homogeneous
and isotropic electric and magnetic properties are presented as the connections
between the generalized magnetization-polarization bivector $%\mathcal{M}$ and
the electromagnetic field F. Using the decompositions of F and $\mathcal{M}$,
it is shown how the polarization vector P(x) and the magnetization vector M(x)
depend on E, B and two different velocity vectors, u - the bulk velocity vector
of the medium, and v - the velocity vector of the observers who measure E and B
fields. These constitutive relations with four-dimensional geometric
quantities, which correctly transform under the Lorentz transformations (LT),
are compared with Minkowski's constitutive relations with the 3-vectors and
several essential differences are pointed out. They are caused by the fact
that, contrary to the general opinion, the usual transformations of the
3-vectors $% \mathbf{E}$, $\mathbf{B}$, $\mathbf{P}$, $\mathbf{M}$, etc. are
not the LT. The physical explanation is presented for the existence of the
magnetoelectric effect in moving media that essentially differs from the
traditional one.
