Rotation measures for extragalactic sources, after selection to emphas
ize the large-scale structure of the Galactic magnetic field, reveal a
striking antisymmetric pattern about the Galactic plane and the merid
ian through the Galactic Centre. This pattern is also observed in the
rotation measures of pulsars with \b\ > 8 degrees. The symmetry of the
pattern, the magnitude of the rotation measures and the distance depe
ndence of the pulsar rotation measures show that this pattern is not t
he result of local perturbations, but is on a large and possibly Galac
tic scale. This antisymmetric pattern and the existence of magnetic fi
elds perpendicular to the plane in the Galactic Centre region, indicat
e that a dynamo mode of odd symmetry, possibly of A0 type, makes a sub
stantial contribution to the magnetic fields in the thick disk and hal
o of our Galaxy, at least inside the Solar circle.