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[en] We present a proposal for a PET detector with a specific design oriented to its application to in-beam treatment monitoring in hadron therapy. The design is focused to the reduction of the uncertainty on the depth of the interaction of the gamma rays in the scintillator to improve the final spatial resolution of the reconstructed images. A small detector prototype, based on two staggered scintillator matrices, was assembled and irradiated with a β+ emitting radioactive source. The obtained results are presented.