Ground state correlations in the Ising model with random ± J bonds are investigated on a square lattice, as a function of the concentration of negative bonds. By comparing all the ground‐states of (18×18) samples, we study the size distribution of packets of solitary spins. Large packets, containing more than half the spins, are observed in most samples, even at maximum bond disorder. This finding implies a remarkable rigidity of the random frustrated system at zero temperature.