We present a preliminary analysis of new high resolution radio observations of the nearby TeV blazar Markarian 421 (z=0.031). This study is part of an ambitious multifrequency campaign, with observations in sub-mm (SMA), optical/IR (GASP), UV/X-ray (Swift, RXTE, MAXI), and gamma rays (Fermi-LAT, MAGIC, VERITAS). In this manuscript we consider only data obtained with the Very Long Baseline Array (VLBA) at seven epochs (one observation per month from January to July 2011) at 15 and 23.8 GHz. We investigate the inner jet structure on parsec scales through the study of model-fit components for each epoch. We identified 5-6 components which are consistent with being stationary during the 6-month period reported here. The aim is to try to shed light on questions such as the nature of radiating particles, the connection between radio and gamma-ray emission, the location of emitting regions and the origin of the flux variability.