  Poincar\'e-Einstein's synchronization convention is transitive, and thus
leads to a consistent synchronization, only if some form of round-trip property
is satisfied. An improved version is given here which does not suffer from this
limitation and which therefore may find application in physics, computer
science and communication theory. As for the application to physics, the
round-trip condition required by the Poincar\'e-Einstein's synchronization
convention corresponds to a vanishing Sagnac effect and thus to the selection
of an irrotational frame. The corrected method applies also to rotating frames
and shows that there is a consistent synchronization for every given measure on
space. The correction to Poincar\'e-Einstein's amounts to an average of the
Sagnac holonomy over all the possible triangular paths. The mathematics used is
reminiscent of Alexander cohomology theory.
