  A combined sample of 79 high and low redshift supernovae Ia (SNe) is used to
set constraints on the degree of anisotropy in the Universe out to $z\simeq1$.
First we derive the global most probable values of matter density $\Omega_M $,
the cosmological constant $\Omega_\Lambda $, and the Hubble constant $H_0$, and
find them to be consistent with the published results from the two data sets of
Riess et al. 1998 (R98) and Perlmutter et al. 1999 (P99). We then examine the
Hubble diagram (HD, i.e., the luminosity-redshift relation) in different
directions on the sky by utilising spherical harmonic expansion. In particular,
via the analysis of the dipole anisotropy, we divide the sky into the two
hemispheres that yield the most discrepant of the three cosmological
parameters, and the scatter $\chi^2_{\rm HD}$ in each case. The most discrepant
values roughly move along the locus $-4\Omega_M +3 \Omega_{\Lambda} = 1$ (cf.
P99), but by no more than $\Delta \approx 2.5$ along this line. For a perfect
FRW universe, Monte Carlo realizations that mimic the current set of SNe yield
values higher than the measured $\Delta$ in $\sim 1/5$ of the cases. We discuss
implications for the validity of the Cosmological Principle, and possible
calibration problems in the SNe data sets.
