A new framework for the development of the perfectly matched layer (PML) in the Transmission Line Modelling (TLM) method is demonstrated. The formulation is based on the stretched coordinate PML and involves the mapping of the TLM node to an analytically extended geometric domain. The implementation demonstrates the more stable second order discretization of the PML equations in TLM. The validity of the PML formulation is demonstrated on a canonical case of a metal waveguide and compared with an existing PML TLM scheme.