Broadband, mid-infrared supercontinuum generation in a step-index fluoroindate fibre is reported. By using ~70-picosecond laser pulses at 2.02 μm, provided by an optical parametric generator, a wide spectrum with a cut-off wavelength at 5.25 μm and a 5-dB bandwidth covering the entire 2-5 μm spectral interval has been demonstrated for the first time. The behaviour of the supercontinuum was investigated by changing the peak power and the wavelength of the pump pulses. This allowed the optimal pumping conditions to be determined for the nonlinear medium that was used. The optical damage threshold for the fluoroindate fibre was experimentally found to be ~200 GW/cm2.