Abstract: Some recent work \cite{jsc} have shown that the «classical» models of Perfectly Matched Layers (PML), typically used as Absorbing Boundary Condition- s in Computational Electromagnetics codes, could lead to long-time linear growth of the solution. We propose here new PML which eliminate this undesirab- le long-time behavior. For these new PML equations, we give energy arguments that show the fields in the layer are bounded by a time-independent constant hence they are long-time stable. Numerical experiments confirm the elimination of the linear growth, and the long-time boundedness of the fields.