The purpose of this work is to correct the mistake that exists in a work previously reported by the author and that claimed an infinite speed of light in vacuum. The proof given in this work for the same result of an infinite speed of light in vacuum solves the electromagnetic problem in two simple lossy media in uniform rectilinear motion with respect to each other. The boundary of the media is an infinite plane perpendicular to the direction of velocity boost. The media are assumed to have equal relaxation times when they are both at rest. In the paper preliminary field quantities are noted and the boundary and initial conditions are stated. It turns out that when the surface charge density on the boundary of the media has a zero initial condition, its time derivative also has to vanish initially. This additional condition brings about the infinite speed of light in vacuum.