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We demonstrate a technique for the fabrication of single-mode perfluorinated polymer optical fiber (PPOF). The PPOF preform is composed of poly-methyl-methacrylate (PMMA)-based outer cladding and a graded-index multimode PPOF as the core. A photosensitive graded-index single-mode PPOF with a core diameter of about 6.6 ??m and cladding diameter of 400 ??m was fabricated. The fiber has a cutoff wavelength of 854 nm and exhibits single-mode characteristics at wavelengths of 1310 and 1550 nm. The transmission loss is less than 0.2 dB/m in the wavelength range of 1410-1540 nm and less than 0.5 dB/m for wavelengths up to 1610 nm, significantly less than the typical transmission loss of ~100 dB/m for PMMA fiber. Another important feature of the PPOF is its low refractive index of 1.34, close to aqueous solution of biomaterials, permitting strong optical coupling for biomedical applications.