We　propose　a　scheme　for　realizing　nonreciprocal　microwave　photon　routing　with　two　cascaded　magnon-cavity　coupled　systems,　which　work　around　the　exceptional　points　of　a　parity-time　(PT)-symmetric　Hamiltonian.　An　almost　perfect　nonreciprocal　transmission　can　be　achieved　with　a　broad　bandwidth,　where　the　transmission　for　a　forward-propagating　photon　can　be　flexibly　controlled　with　the　backpropagating　photon　being　isolated.　The　transmission　or　isolated　direction　can　be　reversed　via　simply　controlling　the　magnetic　field　direction　applied　to　the　magnons.　The　isolation　bandwidth　is　improved　by　almost　three　times　in　comparison　with　the　device　based　on　a　single　PT-symmetric　system.　Moreover,　the　effect　of　intrinsic　cavity　loss　and　added　thermal　noises　is　considered,　confirming　the　experimental　feasibility　of　the　nonreciprocal　device　and　potential　applications　in　quantum　information　processing.　©　2024　Optica　Publishing　Group.　All　rights,　including　for　text　and　data　mining　(TDM),　Artificial　Intelligence　(AI)　training,　and　similar　technologies,　are　reserved.