Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain.That is, the two schemes support common wave solutions with group velocity pointed into the computation domain.The key to eliminate local coupling instability is to avoid such wave solutions.For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided.With a uniform rectangular mesh, it is proven and validated that high-frequency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than 2~(1/2) times the ratio of the P wave velocity to the S wave velocity.These results can be valuable for dealing instability problems induced by other absorbing boundary conditions. Local coupling instability will occur when the numerical scheme of absorbing boundary condition and that of the field wave equation allow energies to spontaneously enter into the computational domain.That is, the two schemes support common wave solutions with group velocity pointed into the computation domain. key to eliminate local coupling instability is to avoid such wave solutions. For lumped-mass finite element simulation of P-SV wave motion in a 2D waveguide, an approach for stable implementation of high order multi-transmitting formula is provided. mesh, it is proven and validated that high-frequency local coupling instability can be eliminated by setting the ratio of the element size equal to or greater than 2 ~ (1/2) times the ratio of the P wave velocity to the S wave velocity These results can be valuable for dealing instability problems induced by other absorbing boundary conditions.