An ESR hyperfine splitting pattern of a biradical in solution depends on the magnitude of the intramolecular exchange interaction J(intra) compared with the hyperfine coupling constant A. Some biradicals exhibit their hyperfine splitting patterns characteristic of a monoradical, even though their exchange interaction is strong enough, vertical bar J(intra)vertical bar >> vertical bar A vertical bar. The contradiction in ESR spectroscopy is known as "biradical paradox", puzzling scientists for a long time. In this study, it is shown from ESR spectral simulations underlain by a theoretical model of a series of spin Hamiltonians that noncovalent aggregation of biradical molecules in solution leads to the appearance of paradoxical ESR spectra. Most of the spins in an aggregate of one dimension lose their contribution to the ESR spectra owing to intermolecular antiferromagnetic interactions J(inter), leaving two outermost spins ESR-active in the aggregate of one dimension. Paradoxical ESR spectra appear only when J(intra) and J(inter) fall within a particular range of the magnitudes which depends on the number of molecules in the aggregate.