In order to tackle the energy hole problem of sensor networks, the non-uniform node deployment strategy was presented recently. For achieving the expected performance of this deployment method, nodes need to transmit data to the sink node through selecting a node in the adjacent inner-region decided by the deployment strategy. Since nodes near the outer-boundary of a region will be covered by more nodes, the random selection method will cause the unbalanced energy consumption problem. In this paper, this issue is rigorously studied and a region constrained selection scheme is proposed based on the analytical result. Numerical and simulation results show that region constrained scheme can achieve acceptable performance improvements over random scheme.