Abstract: The necessary and sufficient condition of late-time stability of time-domain magnetic field integral equations (TDMFIE) based marching on-in time (MOT) algorithm is obtained through theoretical derivation. Using the condition, the late-time stability of TDMFIE-MOT algorithm can be estimated accurately. Based on the condition, an improved algorithm is proposed to ensure that the transient currents are stable in the late-time. The stability condition is validated by numerical results. It is also validated that the improved algorithm is more accurate than TDMFIE-MOT algorithm.