  We present a method to test the isotropy of the magnitude-redshift relation
of Type Ia Supernovae (SNe Ia) and single out the most discrepant direction (in
terms of the signal-to-noise ratio) with respect to the all-sky data. Our
technique accounts for possible directional variations of the corrections for
SNe Ia and yields all-sky maps of the best-fit cosmological parameters with
arbitrary angular resolution. To show its potential, we apply our method to the
recent Union2.1 compilation, building maps with three different angular
resolutions. We use a Monte Carlo method to estimate the statistical
significance with which we could reject the null hypothesis that the
magnitude-redshift relation is isotropic based on the properties of the
observed most discrepant directions. We find that, based on pure
signal-to-noise arguments, the null hypothesis cannot be rejected at any
meaningful confidence level. However, if we also consider that the strongest
deviations in the Union2.1 sample closely align with the dipole temperature
anisotropy of the cosmic microwave background, we find that the null hypothesis
should be rejected at the $95-99$ per cent confidence level, slightly depending
on the angular resolution of the study. If this result is not due to a
statistical fluke, it might either indicate that the SN data have not been
cleaned from all possible systematics or even point towards new physics. We
finally discuss future perspectives in the field for achieving larger and more
uniform data sets that will vastly improve the quality of the results and
optimally exploit our method.
