High-resolution radio observations are ideal for constraining the value of physical parameters in the inner regions of active-galactic- nucleus jets and complement results on multiwavelength observations. The aim of their wider multifrequency campaign is to try to shed light on questions such as the nature of the radiating particles, the connection between the radio and gamma -ray emission, the location of the emitting regions and the origin of the flux variability. The authors consider data obtained with the Very Long Baseline Array over twelve epochs at 15 GHz and 24 GHz. The structure of Mrk 421 is dominated by a compact similar to 0.13 mas and bright component, with a one-sided jet detected out to similar to 10 mas. The authors identify 5-6 components in the jet that are consistent with being stationary during the 12-month period studied here. Measurements of the spectral index agree with those of other works: they are fairly flat in the core region and steepen along the jet length.