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Cryptocurrencies such as Bitcoin and Ethereum have made payment transactions possible without a trusted third party, but they have a scalability issue due to their consensus mechanisms. Payment networks have emerged to overcome this limitation by executing transactions outside of the blockchain, which is why these are referred to as off-chain transactions. In order to establish a payment channel between two users, the users lock their deposits in the blockchain, and then they can pay each other through the channel. Furthermore, payment networks support multi-hop payments that allow users to transfer their balances to other users who are connected to them via multiple channels. However, multi-hop payments are hard to be accomplished, as they are heavily dependent on routing users on a payment path from a sender to a receiver. Although routing hubs can make multi-hop payments more practical and efficient, they need a lot of collateral locked for a long period and have privacy issues in terms of payment history. We propose RouTEE, a secure payment routing hub that is fully feasible without the hub's deposit. Unlike existing payment networks, RouTEE provides high balance liquidity, and details about payments are concealed from hosts by leveraging trusted execution environments (TEEs). RouTEE is designed to make rational hosts behave honestly, by introducing a new routing fee scheme and a secure settlement method. Moreover, users do not need to monitor the blockchain in real-time or run full nodes. They can participate in RouTEE by simply verifying block headers through light clients; furthermore, having only one channel with RouTEE is sufficient to interact with other users. Our implementation demonstrates that RouTEE is highly efficient and outperforms Lightning Network that is the state-of-the-art payment network.