Our earlier joint analysis of light curves for the blazar 0059+581 at 4.8, 8, 14.5, 22, and 37 GHz with high-resolution VLBI images led us to suggest that the activity in this source develops in cycles, or periods, with a duration of about four years, with a "typical scenario" for the development of the source's activity taking place over a cycle. Based on this analysis, we predicted in 2002 that a new superluminal component would be ejected from the core of this source in a structural position angle ∼170° no later than by the end of 2003. A 43-GHz VLBI image obtained on September 14, 2003, as part of a program to monitor the structure of reference sources used for a radio astronomical coordinate system, convincingly confirms the correctness of this prediction. This is the first time in the history of radio astronomy that a new superluminal component has been detected at a predicted time and in a predicted structural position angle.