A formalism for extracting coupled betatron parameters from multiturn, shock excited, beam position monitor data is described. The most important results are nonperturbative in that they do not rely on the underlying ideal lattice model. Except for damping, which is assumed to be exponential and small enough to be removed empirically, the description is symplectic. As well as simplifying the description, this leads to self‐consistency checks that are applied to the data. The most important of these is a ‘‘magic ratio’’ of Fourier coefficients that is required to be a lattice invariant, the same at every beam position monitor. All formulas are applied to both real and simulated data. The real data were acquired June 1992 at LEP as part of decoupling studies, using the LEP beam orbit measurement system. Simulated data, obtained by numerical tracking (TEAPOT) in the same (except for unknown errors) lattice, agrees well with real data when subjected to identical analysis. For both datasets, deviations between extracted and design parameters and deviations from self‐consistency can be accounted for by noise and signal‐processing limitations. This investigation demonstrates that the LEP beam position system yields reliable local coupling measurements. It can be conservatively assumed that systems of similar design at the SSC and LHC will provide the measurements needed for local decoupling.