Users in secondary multi-hop networks have to select paths and obtain spectrum for the selected paths to deliver their traffic. We consider a case that users obtain TV white spaces from a geo-location database for their selected paths at some cost. To reduce the cost of routing, users will reuse their spectrum along the paths. Due to link diversity, redundant spectrum exists on some links. To further improve spectrum utilization in the network, we propose a Nash bargaining based spectrum sharing rule for users to share and reduce redundant spectrum. Analytical and simulation results show that our proposal reduces the total spectrum requirement in the network.