The BL Lac object Markarian 421 (Mk 421) has been mapped using VLBI arrays at a wavelength of 6 cm on four epochs from 1980.41 to 1983.43. It has a core-jet like structure with the jet pointing to the direction of NW with a stable position angle of about -45 deg. Almost all of the flux variation is accounted for by the change of the peak flux density of a compact component in the core. The results show that Mk 421 may exhibit apparent superluminal motion with apparent transverse speeds of components of (1.92 + or - 0.03)c (from 1981.25 to 1981.94) and (1.79 + or - 0.23)c (from 1981.94 to 1983.43) for C1; and (1.36 + or - 0.22)c for C2. The position angles of both the components C1 and C2 are nearly the same as the position angle of the jet, and there is no significant change of position angle as they move away from the core.