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The throughput of a communication system depends on the data traffic load and the available capacity to support that load. In an unmanned aerial vehicle (UAV)-based communication system, the UAV position is one of the major factor affecting the capacity available to the flows (data sessions) being served. This paper proposes a centralized algorithm for positioning UAVs to maximize the throughput of a software-defined disaster area UAV communication network. The software-defined networking controller maintains upto date information about the network topology as well as the data rate demands and paths of the flows. The proposed algorithm utilizes this information to determine the positions for the UAVs such that the total throughput is maximized. The algorithm was simulated using MATLAB. The results showed that an average throughput improvement of 26% can be achieved by optimally positioning the UAVs.