We study the assembly of spherical particles with opposite electric charge on both hemispheres, in the case that the particle diameter exceeds the electrostatic screening length. Clusters result, not strings. The cluster shapes are analyzed by combined epifluorescence microscopy and Monte Carlo computer simulations with excellent agreement, indicating that the particles assemble in aqueous suspension to form equilibrated aggregates. The simulations show that charge asymmetry of individual Janus particles is preserved in the clusters.