Global analysis of fluorescence lifetime image microscopy (FLIM) data can be used to obtain an accurate fit of multi-exponential fluorescence decays. In particular, it can be used to fit a bi-exponential decay to single frequency FLIM data, which is not possible with conventional fitting techniques. Bi-exponential fluorescence decay models can be used to analyse quantitatively single frequency FLIM data from samples that exhibit fluorescence resonance energy transfer (FRET). Global analysis algorithms simultaneously fit multiple measurements acquired under different experimental conditions to achieve higher accuracy. To demonstrate that bi-exponential models can indeed be fitted to single frequency data, we derive an analytical solution for the special case of two measurements and use this solution to illustrate the properties of global analysis algorithms. We also derive a novel global analysis algorithm that is optimized for single frequency FLIM data, and demonstrate that it is superior to earlier algorithms in terms of computational requirements.