We apply a statistical method to derive very precise locations for soft gam
ma repeaters using data from the interplanetary network. We demonstrate the
validity of the method by deriving a 600 arcsec(2) error ellipse for SGR 1
900+14 whose center agrees well with the VLA source position. We then apply
it to SGR 1806-20, for which we obtain a 230 arcsec(2) error ellipse, the
smallest burst error box to date. We find that the most likely position of
the source has a small but significant displacement from that of the nonthe
rmal core of the radio supernova remnant G10.0-0.3, which was previously th
ought to be the position of the repeater. We propose a different model to e
xplain the changing supernova remnant morphology and the positions of the l
uminous blue variable and the bursting source.