Node mobility is one of the dominant factors causing decreased performance in mobile ad hoc networks, thus stability of selected path is of prime importance. The proposed method uses link stability factor (LSF) and path stability factor (PSF) to select a stable path while minimizing number of hops. The node's transmission range is divided into stable zone and caution zone. Rerouting is initiated when the distance between two neighboring communicating nodes exceeds the stable zone, before the old path actually breaks, thus realizing soft handoff and reducing the data packet's ETE delay. The proposed LSB_AODV routing scheme is evaluated by simulation and results show that an improved packet delivery ratio and reduced ETE delay can be obtained.