An old but still unsolved problem was to show that in the critical dimension, the Brownian sheet does not have multiple points. Recent work of Dalang, Khoshnevisan, and Xiao established that for a broad class of multiple points, the assertion is true. This class included many, but not all possible multiple points. In particular, the time parameters had a particular order relation. In this work, joint with Robert Dalang, we deal with the general situation by showing that there are no multiple points for the Brownian sheet in the critical case.