The cluster algorithm in the fully frustrated Ising model on the squar
e 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 ou
r simulations of high statistics more appropriate choices of the proba
bility for freezing bonds and of that for flipping spins are seen to l
ead 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.