We present a method for the determination of dissociation energies of polyatomic systems that undergo sequential fragmentation with energy-dependent decay pathway branching. It allows to experimentally determine the dissociation energy of any polyatomic system that shows such fragmentation behaviour without the need for a specific modelling of the system or of its fragmentation process, thus eliminating several systematic errors of traditional methods. The new method has been applied to the sequential fragmentation of Au-14(+) and Au-16(+). The resulting dissociation energies are highly accurate and in good agreement with model-free values based on rates of sequential decays.