A monolithic crystal-based positron emission tomography (PET) detector has a low cost and high sensitivity and allows determining 3D positions by scintillation light distribution. However, the edge effect inherent to scintillators deteriorates the position resolution of the detector toward the crystal borders due to the escape and reflection of the scintillation light. An increase in crystal thickness will improve the detection efficiency, but the edge effect becomes severe. To improve the position resolution and detection efficiency of scintillators, the light-sharing technique is developed. Two identical trapezoidal monolithic cerium-doped lutetium yttrium orthosilicate (LYSO) crystals with a bottom size of 25.80 x 25.80mm(2) and a thickness of 20mm are optically coupled at one lateral face by an optical medium. The scintillation light near the optically coupled interface is jointly collected by two adjacent 8 x 8 SiPM arrays from the bottom faces. The SiPM signals are individually read out and processed by using the multichannel readout application-specific integrated circuits (ASICs) of TOFPET2 to provide a light distribution. The transverse positions and depth of interaction (DOI) are calculated from the measured light distribution. As expected, the optical glue with a refractive index of n = 1.68 shows better light sharing between two LYSO crystals than the coupling media of silicon grease (n = 1.40) and air. For the 20 mm thick monolithic LYSO-based PET detector, the transverse position resolution near the crystal edge is improved by nearly 30% by using the light-sharing method compared with the black-painted treatment. However, the DOI resolution near the edge of the crystal is not significantly improved, which may be attributed to the incomplete collection of scintillation light. The DOI resolution of the detector would be improved by using electronics with lower noise and SiPM arrays with smaller pixel.