The photodissociation processes of the manganese cluster ions Mn-n(+) (n=3 and 4) were investigated in the visible and near-infrared photon-energy ranges. The threshold energies were determined for the two-atom-loss channels by measurements of the spectra of the partial photodissociation cross sections. The binding energies of Mn-n(+) (n=3 and 4) were obtained by using these threshold energies and the known bond dissociation energy of Mn-2(+). The bond dissociation energies of Mn-3(+), D-0(Mn-2(+).Mn), and Mn-4(+), D-0(Mn-3(+).Mn), were determined to be 0.83+/-0.05 and 1.04+/-0.07 eV, respectively. Thus the binding energies (per atom) of Mn-3(+) and Mn-4(+) turned out to be 0.74+/-0.03 and 0.82+/-0.05 eV, respectively. These findings show that the interaction between manganese atoms is exceptionally weak, compared with other transition-metal cluster ions.