  We present four high dynamic range, dual-circular polarization, Very Long
Baseline Array (VLBA) observations at 22 GHz of Markarian 421, taken throughout
the year following the source's unprecedented gamma-ray high state in early
2001. These four new VLBA observations are combined with data from our earlier
1999 paper and archival VLBA data-sets that have become available since 1999 to
produce a combined 28 epoch VLBA data-set on Mrk 421 spanning the years 1994 to
2002. No new component associated with the 2001 flares was seen on the total
intensity images, but the combined data-set allowed precise measurements of the
apparent speeds of the existing components. The peak measured apparent speed
was for component C5, which has an apparent speed of 0.1 +/- 0.02 c (H_0=71 km
s^{-1} Mpc^{-1}, Omega_m=0.27, and Omega_Lambda=0.73). No counterjet is seen
with a limit on the jet to counterjet brightness ratio J >~ 100. These observed
VLBI properties of Markarian 421 are consistent with a jet with a bulk Lorentz
factor of about 2 and an angle to the line-of-sight of about 1 degree,
suggesting a jet that decelerates between the gamma-ray producing region and
the parsec scale. The VLBI core and inner jet (component C7) have fractional
polarizations of about 5%, and an electric vector position angle (EVPA) aligned
with the jet axis. Component C5 (at 1.5 mas from the core) has a higher
fractional polarization of about 15%, and an EVPA nearly orthogonal to the jet
axis. Significant variability is detected in the EVPA of component C6, which at
two of the four epochs shows an EVPA aligned with the jet axis, possibly a sign
of propagating disturbances that are only visible on the polarization images.
If these propagating disturbances are linked to the 2001 gamma-ray high state,
then their inferred apparent speed is between 1 and 3 c.
