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Previously, we proposed a new depth of interaction (DOI) encoding method and proved that it worked successfully with four-layered Gd2SiO5 crystals for a small animal positron emission tomography (PET) detector. We are now planning to develop a small animal PET scanner, jPET-RD (for rodents with DOI detectors), which has both high resolution and high sensitivity by the use of a DOI detector with a 32×32×4 crystal array. The scintillator for the detector will be Lu2(1-x)Y2xSiO5 (LYSO). In this work, we evaluated performance of a DOI detector composed of four layers of a 12×12 LYSO (Lu: 98%, Y: 2%) crystal array by irradiating 511 keV gamma rays uniformly. The new encoding method was used for crystal identification. The size of each crystal was 1.46 mm×1.46 mm×4.5 mm. The crystal block was coupled to a 256-channel flat panel position sensitive photomultiplier tube, which has 16×16 multi anodes at intervals of 3.04 mm. As we expected, all crystals are expressed on a single two-dimensional position histogram without overlapping. Energy resolution of all events is 21.8% and time resolution of all events is 0.69 ns in FWHM. When layers are counted from the top, the energy resolutions of the first, second, third, and fourth layer events are 11.6%, 12.3%, 13.3%, and 19.1% and the time resolutions are 0.60ns, 0.59ns, 0.60ns, and 0.66ns, respectively.