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Using the optical spectrum obtained with the Kitt Peak Ohio StateMulti-Object Spectrograph (KOSMOS) mounted on the Apache Point Observatory(APO) 3.5m Telescope and the Sloan Digital Sky Survey (SDSS) spectrum, we studythe properties of one of the most metal-poor dwarf star-forming galaxies (SFG)in the local Universe, J1046+4047. The galaxy, with a redshift z=0.0487, wasselected from the Data Release 16 (DR16) of the SDSS. Its properties are amongthe most extreme for SFGs in several ways. Its oxygen abundance 12+log(O/H) =7.091+/-0.016 is among the lowest ever observed. With an absolute magnitude Mg= -16.51 mag, a low stellar mass Mstar = 1.8x10^6 Msun and a very lowmass-to-light ratio Mstar/Lg~0.0029 (in solar units), J1046+4047 has a veryhigh specific star-formation rate sSFR~430 Gyr^-1, indicating very activeongoing star formation. Another striking feature of J1046+4047 is that itpossesses a ratio O32 = I([OIII]5007)/I([OII]3727) ~57. Using this extremelyhigh O32, we have confirmed and improved the strong-line calibration for thedetermination of oxygen abundances in the most metal-deficient galaxies, in therange 12+log(O/H) < 7.65. This improved method is appropriate for all galaxieswith O32<60 and extends an applicability to highest observed O32 ratios.We findthe Halpha emission line in J1046+4047 to be enhanced by some non-recombinationprocesses and thus can not be used for the determination of interstellarextinction.

J1046+4047: an extremely low-metallicity dwarf star-forming galaxy with O32 = 57