One significant problem of transboundary river basins causing various challenges and disputes throughout the world is that because of increasing water resource variability and consumption, the water demand often exceeds water availability. Hence, one of the main challenges in transboundary river basin management is how to allocate the available water among the riparian states equitably and reasonably. In this study, we propose a novel weighted bankruptcy solution method to cope with the problem of demands or “claims” exceeding resources or “assets”. Certain desirable key properties of the proposed method are provided. Furthermore, we investigate its application to the Tigris River, a shared river among Turkey, Syria and Iraq, as a real case. The available water is allocated under two different situations: homogeneous and heterogeneous group. We use the Shapley Value and compare the solution with other allocation methods applied in this study. The results suggest that this new rule may facilitate negotiation in solving conflict over the allocation of water in transboundary river basins.