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 \pm 0.27 , 0.30 \pm 0.07 , and - 0.07 \pm 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 & Bååth 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 .