We analyze the spectrum of an unusually-low mass white dwarf , SDSSJ123410.37-022802.9 ( 0335-264-52000 ) , found in our recent , white dwarf catalog from the SDSS DR1 data release . Two independent , model atmosphere fits result in an accurate determination of atmospheric and stellar parameters . The more hands-on analysis yields T _ { eff } = 17,470 \pm 750 K and \log g = 6.38 \pm 0.05 . We argue that the object can not be a main sequence A star , a horizontal branch or subdwarf B star . Instead , it is interpreted as a very low mass white dwarf with a core composed of helium , with mass ( \sim 0.18-0.19 M _ { \odot } ) , similar to that published previously for the unusual companion to the millisecond pulsar J1012+5307 . The star probably remains in a binary , perhaps even with an undiscovered or dead pulsar companion . However , the companion might be a more-ordinary star , provided Roche lobe mass transfer began shortly after the now-visible component left the main sequence . A second SDSS low mass white dwarf candidate is also analyzed , but the spectrum for this fainter object is of poorer quality . The sample appears to include additional , similar candidates , worthy of more accurate observation . Correct identification of any additional white dwarfs of extremely low mass requires careful observation and interpretation .