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1/2 network capacity is often believed to be the limit of worst-case throughput for mesh networks. However, this letter provides a new worst-case throughput bound, which is higher than 1/2 network capacity, for odd radix two-dimensional mesh networks. In addition, we propose a routing algorithm called U2TURN that can achieve this worst-case throughput bound. U2TURN considers all routing paths with at most 2 turns and distributes the traffic loads uniformly in both X and Y dimensions. Theoretical analysis and simulation results show that U2TURN outperforms existing routing algorithms in worst-case throughput. Moreover, U2TURN achieves good average-throughput at the expense of approximately 1.5x minimal average hop count.