The localizations of gamma-ray bursts (GRBs) detected with the Gamma-ray
Burst Monitor (GBM) onboard the Fermi satellite are known to be affected by
significant systematic errors of 3-15 degrees. This is primarily due to
mismatch of the employed Band function templates and the actual GRB spectrum...
This problem can be avoided by simultaneously fitting for the location and the
spectrum of a GRB, as demonstrated with an advanced localization code, BALROG
(arXiv:1610.07385). Here, we analyze in a systematic way a sample of 105 bright
GBM-detected GRBs for which accurate reference localizations are available from
the Swift observatory. We show that the remaining systematic error can be
reduced to $\sim$1-2 degrees.