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This paper reports on a 4H-SiC single-photon avalanche diode (SPAD) operating at UV wavelengths of 280 and 350 nm. The SPAD shows low dark currents of 20 and 57 fA at 80 V and 90% breakdown voltage, respectively. The quantum efficiency (QE) reaches its peak of 43% at 270 nm and is < 0.007% at 400 nm, indicating a high UV-to-visible rejection ratio of > 6100. The 4H-SiC SPAD shows a fast self-quenching and a high photon count rate of 1.44 MHz in the passive-quenching mode. At the wavelength of 280 nm, a single-photon detection efficiency (SPDE) of 2.83 % with a low dark count rate of 22 kHz is achieved at the reverse bias of 116.8 V. The SPDE at 350 nm is lower, which is 0.195%, owing to the correspondingly smaller QE. Optimization measurements were conducted on SPDE as a function of voltage bias and signal output threshold.