The domain wall (DW) velocity above the Walker field drops abruptly with increasing magnetic field, because of the so-called Walker breakdown, where the DW moves with a precessional mode. On applying the higher field, the DW velocity again starts to increase gradually. We report the DW propagation around this local minimum regime in detail, investigated through the time-resolved electrical detection technique, with a magnetic tunnel junction. Just above the Walker field, we succeeded in detecting the precessional motion of the DW in a real-time regime, while a different mode appeared around the local minimum of the DW velocity.