  We present thirty VLBI images of the TeV blazar Markarian 421 (1101+384) at
fifteen epochs spanning the time range from 1994 to 1997, and at six different
frequencies from 2.3 to 43 GHz. The imaged observations include a
high-resolution 5 GHz VLBI Space Observatory Programme (VSOP) observation with
the HALCA satellite on 1997 November 14; full-track VLBA observations from 1994
April, 1996 November, and 1997 May at frequencies between 5 and 43 GHz; six
epochs of VLBA snapshot observations at frequencies between 2 and 15 GHz from
Radio Reference Frame studies; and five geodetic VLBI observations at 2 and 8
GHz from the archive of the Washington VLBI Correlator Facility located at the
U.S. Naval Observatory. The dense time coverage of the images allows us to
unambiguously track components in the parsec-scale jet over the observed time
range. We measure the speeds of three inner jet components located between 0.5
and 5 mas from the core (0.3 to 3 pc projected linear distance) to be 0.19 +/-
0.27, 0.30 +/- 0.07, and -0.07 +/- 0.07 c (H_{0}=65 km s^{-1} Mpc^{-1}). If the
sole 43 GHz image is excluded, all measured speeds are consistent with no
motion. These speeds differ from tentative superluminal speeds measured by
Zhang & B\aa\aa th from three epochs of data from the early 1980's. Possible
interpretations of these subluminal speeds in terms of the high Doppler factor
demanded by the TeV variability of this source are discussed.
