A procedure is developed which leads to a relation that can be used to argue the negation of the Special Relativity Theory when there exists a general homogeneous bianisotropic medium with dissipation. The unbounded general bianisotropic medium is interfaced with a perfectly conducting medium filling a half space so that the interface is an infinite plane. The perfectly conducting half space (medium (II)) is assumed to move uniformly and along the O'z' axis of the Galilean reference system K' which is attached to medium (II), and the interface plane with medium (I), the bianisotropic medium which is at rest and to which is attached the Galilean reference system K, is assumed to be perpendicular to the O'z' axis. The relation found is between constitutive parameters, the direction cosines with respect to Oxyz axes of the incident plane wave impingent on the infinite plane interface, the incident wave parameters, vi the relative speed of K' with respect to K and c the speed of light in vacuum. This relation is shown to be interpretable to falsify the Special Relativity Theory. On the other hand it is demonstrated also that when the same homogeneous bianisotropic medium without loss is considered no such relation can be obtained and the Special Relativity Theory cannot be contradicted.