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.