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We report an octave-spanning coherent supercontinuum (SC) fiber laser with excellent noise and polarization properties. This was achieved by pumping a highly birefringent all-normal dispersion photonic crystal fiber with a compact high-power ytterbium femtosecond laser at 1049 nm. This system generates an ultra-flat SC spectrum from 670 to 1390 nm with a power spectral density higher than 0.4 mW/nm and a polarization extinction ratio of 17 dB across the entire bandwidth. An average pulse-to-pulse relative intensity noise down to 0.54% from 700 to 1100 nm was measured and found to be in good agreement with numerical simulations. This highly stable broadband source could find strong potential applications in biomedical imaging and spectroscopy where an improved signal-to-noise ratio is essential.