Absorption spectra of a hemicyanine monolayer on a sodium sulfate subphase were recorded as a function of surface pressure. Upon compression, the intensity of the monomer band is reduced and two new bands are observed. The results from principal factor analysis of the spectra and the clear isosbestic points indicate that the two bands are due to exciton splitting from an aggregate structure with two molecules per unit cell. By comparison with spectra obtained previously, the influence of counterions and the dilution of the dye monolayer on the formation and structure of the aggregates is investigated. The addition of sulfate counterions to the subphase raises the threshold surface concentration for the formation of aggregates, and produces an aggregate structure in which one long molecular axis is oriented closer to the surface normal. Dilution of the dye monolayer results in a small change to the aggregate structure. Furthermore, if it is assumed that the dye-diluent monolayer is inhomogeneous, dilution has no significant effect on the surface concentration dependence of the formation of aggregates.