The monomer and aggregate of the squaraine dye bis(2,4,6,-trihydroxyphenyl)squaraine (SQ) form weak complexes with triplet sensitizers such as benzophenone and 1-pyrenecarboxaldehyde. Excitation of the complex results in static triplet energy transfer from the sensitizer to the monomer and aggregate of SQ. The aggregate triplet undergoes unimolecular decay to its ground state (tau = 6.7 mu s), whereas self-quenching of the monomer triplet state results in the formation of the aggregate ground state. The aggregate formed in this process undergoes a slow decay (tau = 0.69 ms) to establish the ground-state monomer-aggregate equilibrium.