The best coverage problem is finding a path whose worst distance to the sensor-set is the best among all paths. Instead, if the user stays close to its nearest two sensors, then the stability of the wireless connection may be guaranteed. So we consider the problem of finding a second best coverage path; given the sensor set U, a starting point s and a target point t, find a path whose worst distance to the second closest sensor is minimized. This paper presents an O(n logn) -time algorithm to find such a path. We also give experimental evidence showing that the connection to the sensor-set along a second best coverage path is more stable than that along the best coverage path.