The stability of polynuclear superhalogen anions composed of BiF5 building blocks was investigated using ab initio electronic structure methods and flexible basis sets. A comprehensive exploration of the ground state potential energy surfaces of (Bi2F11)−, (Bi3F16)− and (Bi4F21)− anions, which can be viewed as comprising BiF5 fragments and an additional fluorine atom, led to the identification of their isomeric structures. It was found that the most stable isomers, predicted to dominate at room temperature, correspond to chain-like extended structures containing BiF6 subunits, with fluorine ligands arranged octahedrally around Bi atoms, sharing F atoms to form Bi–F–Bi bridging linkages. The vertical electron detachment energies of the (BinF5n+1)− anions (n = 1–4) were found to be very high (ranging from 10.91 to 13.36 eV) and increased with the number of bismuth atoms (n) and thus the BiF5 building blocks involved in the structure. Thermodynamic stability of the (BinF5n+1)− anions (i.e., their susceptibility to fragmentation) was also verified and discussed.