It is shown that the anisotropic perfectly matched medium, proposed recently for the construction of reflectionless absorbing boundaries for differential equation-based electromagnetic simulations in unbounded domains, can be made equivalent to the Chew-Weedon perfectly matched medium developed from a modified Maxwell's system with coordinate stretching, Consequently, despite the apparently nonphysical coordinate stretching, Chew-Weedorn's formulation, with an appropriate definition of the involved electric and magnetic fields, is. merely an alternative mathematical form of Maxwell's system in an anisotropic medium. Finally, a more convenient time-domain implementation of the perfectly matched layer without splitting of the field components is derived.