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Non-Line-of-Sight (NLOS) Ultraviolet (UV) communication uses the atmosphere as a propagation medium. As the communication range increases, turbulence becomes a significant atmospheric process that affects the propagation of optical waves. This paper presents a more accurate NLOS channel model by considering turbulence-induced Scintillation Attenuation (SA). Then, the Bit Error Rate (BER) during turbulence of the NLOS UV communication system with On-Off Keying (OOK) modulation and Maximum Likelihood (ML) detection is analysed and compared with that in free space without turbulence. The BER dependence is also analysed for different factors, including the refractive index structure parameter, transceiver range, pointing angles, transmitted power, and data rate.