The incidence of an inhomogeneous plane wave on the interface between two lossy media is analyzed. The analytical expressions of the incidence angle of the phase vector, for which the transmitted wave has the phase or the attenuation vector parallel to the interface, are obtained. The transmitted wave with the attenuation vector parallel to the interface is physically interpreted, finding a wave in a lossy medium without attenuation away from the interface. The same effect appears at the interface between a lossless medium and a lossy one.