  The cluster algorithm in the fully frustrated Ising model on the square
lattice is essentially different from the ones used in other systems. Thus its
better understanding is particularly important for finding new lines of
development. Therefore we investigate it in detail. In our simulations of high
statistics more appropriate choices of the probability for freezing bonds and
of that for flipping spins are seen to lead to better results. In an analysis
of the topological properties we derive a set of rules for possible cluster
configurations and give a classification by pairs of winding numbers.
