The　Multi-Transmitting　Formula　(MTF)　proposed　by　Liao　et　al.　is　a　local　artificial　boundary　condition　widely　used　in　numerical　simulations　of　wave　propagation　in　an　infinite　medium,　while　the　drift　instability　is　usually　caused　in　its　numerical　implementation.　In　view　of　a　physical　interpretation　of　the　Gustafsson,　Kreiss　and　Sundström　criterion　on　numerical　solutions　of　initial-boundary　value　problems　in　the　hyperbolic　partial　differential　equations,　the　mechanism　of　the　drift　instability　of　MTF　was　discussed,　and　a　simple　measure　for　eliminating　the　drift　instability　was　proposed　by　introducing　a　modified　operator　into　the　MTF.　Based　on　the　theory　of　spherical　wave　propagation　and　damping　effect　of　medium,　the　physical　implication　on　modified　operator　was　interpreted.　And　the　effect　of　the　modified　operator　on　the　reflection　coefficient　of　MTF　was　discussed.　Finally,　the　validity　of　the　proposed　stable　implementation　measure　was　verified　by　numerical　tests　of　wave　source　problem　and　scattering　problem.