  We present a reanalysis of the VIRMOS-Descart weak lensing data, with a
particular focus on different corrections for the variation of the point spread
function anisotropy (PSF) across the CCDs. We show that the small scale
systematics can be minimised, and eventually suppressed, using the B mode
(curled shear component)measured in the corrected stars and galaxies. Updated
cosmological constraints are obtained, free of systematics caused by PSF
anisotropy. To facilitate general use of our results, we provide the two-points
statistics data points with their covariance matrices up to a scale of one
degree. For the normalisation of the mass power spectrum we obtain
sigma_8=(0.83\pm 0.07)(Omega_M/0.3)^(-0.49). The shape parameter Gamma was
marginalised over Gamma=[0.1,0.3] and the mean source redshift z_s over
[0.8,1.0]. The latter is consistent with recent photometric redshifts obtained
for the VIRMOS data and the preliminary spectroscopic redshifts from the
VIRMOS-VVDS survey. The quoted 68% contour level includes all identified
sources of error. We discuss the possible sources of residual contamination in
this result: the effect of the non-linear mass power spectrum and remaining
issues concerning the PSF correction. Our result is compared with the first
release of the Wilkinson Microwave Anisotropy Probe data. It is found that Cold
Dark Matter models with a power law primordial power spectrum and high matter
density Omega_M > 0.5 are excluded at 3-sigma.
