A new superconducting phase, Bi2Sr2Ca2Cu3O8F4, was obtained by fluorination of standard Bi(2223) at moderate temperatures (250-300 °C), using as fluorine source ammonium hydrogen difluoride, NH4HF2. The presence of fluorine in this new phase was confirmed by energy-dispersive X-ray analysis. X-ray and neutron diffraction experiments furthermore showed that fluorine atoms replace oxygen atoms in the BiO layers in the ratio 2:1. The additional anions form a square-mesh layer between neighboring BiF layers. The incorporation of fluorine increases the crystallographic c-axis parameter by approximately 1.8 angstroms (a = 5.409 angstroms, b = 5.407 angstroms, c = 38.792 angstroms). The CuO2 layers remain undistorted but the distance from the Cu atom to the apical oxygen atom of the square pyramids is decreased to 2.27 angstroms, with respect to 2.42 angstroms in the original phase. The superconducting transition temperature, determined from magnetic susceptibility measurements, was found to be 75 K. When applied to Bi(2212), the same fluorination process produced the new phase Bi2Sr2CaCu2O6F4 with similar structural features.