  We make use of an improved existence result for the characteristic initial
value problem for the conformal Einstein equations to show that given initial
data on two null hypersurfaces $\mathcal{N}_\star$ and $\mathcal{N}'_\star$
such that the conformal factor (but not its gradient) vanishes on a section of
$\mathcal{N}_\star$ one recovers a portion of null infinity. This result
combined with the theory of the hyperboloidal initial value problem for the
conformal Einstein field equations allows to show the semi-global stability of
the Minkowski spacetime from characteristic initial data.
