We investigate the location of the radio jet bases (radio cores) of blazars in radio images, and their stationarity by means of dense very long baseline interferometry (VLBI) observations. In order to measure the position of a radio core, we conducted 12 epoch astrometric observation of the blazar Markarian 421 with the VLBI Exploration of Radio Astrometry at 22 GHz immediately after a large X-ray flare, which occurred in the middle of 2011 September. For the first time, we find that the radio core is not stationary but rather changes its location toward 0.5 mas downstream. This angular scale corresponds to the de-projected length of a scale of $10^5$ Schwarzschild radii (Rs) at the distance of Markarian~421. This radio-core wandering may be a new type of manifestation associated with the phenomena of large X-ray flares.
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