  We investigate the polarization and proper motion expected in a beamed
Gamma-Ray Burst's ejecta. We find that even if the magnetic field has well
defined orientation relative to the direction of motion of the shock, the
polarization is not likely to exceed 20%. Taking into account the dynamics of
beamed ejecta we find that the polarization rises and decays with peak around
the jet break time (when the Lorentz factor of the flow is comparable to the
initial opening angle of the jet). Interestingly, we find that when the offset
of the observer from the center of the beam is large enough, the polarization
as function of time has three peaks, and the polarization direction of the
middle peak is rotated by 90 degrees relative to the two other peaks. We also
show that some proper motion is expected, peaking around the jet break time.
Detection of both proper motion and the direction of polarization can determine
which component of the magnetic field is the dominant.
