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We describe a coded aperture gamma-ray imager that uses a CsI(Na) scintillator coupled to a Hamamatsu R3292 position-sensitive photomultiplier tube (PSPMT) as the position-sensitive detector. We have modified the normal resistor divider readout of the PSPMT to allow use of nearly the full 10-cm diameter active area of the PSPMT with a single scintillator crystal 1 cm thick. This is a significant performance improvement over that obtained with the standard readout technique where the linearity and position resolution start to degrade at radii as small as 3.0 cm with a crystal 0.75 cm thick. This represents a recovery of over 60% of the PSPMT active area. The performance increase allows the construction of an imager with a field of view 20 resolution elements in diameter with useful quantum efficiency from 60-700 keV. In this paper, we describe the readout technique, its implementation in a coded aperture imager, and the performance of that imager.