The hyperfine electron-nuclear interaction in antiferromagnetic rhombic binuclear exchange clusters in the triplet state (S = 1) is considered. The second-order corrections to the hyperfine energy levels and the probabilities of allowed (ΔM = 1, Δm1 + Δm2 = 0) and different types of "forbidden" (ΔM = 1, 2; Δm1 + Δm2 = 0, 1, 2) EPR transitions for canonical orientations of the external magnetic field are calculated. It is shown that the relative line intensities of "parallel" low- and high-field fine transitions depend on the parameter of rhombicity Ei. The hyperfine structure of the low-field transition is predicted to be equally spaced. The EPR spectra of (Cu[(CH3)2CHCOO]2 · 0.5C4H8O2)2 single crystals were studied and explained on the basis of the calculated results obtained.