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We develop a new false-name-proof double auction protocol called the Generalized Threshold Price Double auction (GTPD) protocol. False-name-proofness generalizes strategy-proofness by incorporating the possibility of false-name bids, e.g., bids submitted using multiple e-mail addresses. An existing protocol called TPD protocol is false-name-proof but can handle only the cases where marginal utilities of each agent always decrease, while our new GTPD protocol can handle arbitrary evaluation values. When marginal utilities can increase, some bids cannot be divided into a single unit (e.g., an all-or-nothing bid). Due to the existence of such indivisible bids, meeting supply/demand becomes difficult. Furthermore, a seller/buyer can submit a false-name-bid by pretending to be a potential buyer/seller to manipulate allocations and payments.In the GTPD protocol, the auctioneer is required to absorb the supply-demand imbalance up to a given upper-bound. Also, the GTPD incorporate a new false-name-proof one-sided auction protocol that is guaranteed to sell/buy a certain number of units. Simulation results show that when the threshold price is set appropriately, this protocol can obtain a good social surplus, and the number of absorbed units is much smaller than the given upper-bound.