  Polarization measurements provide a detailed method to test the Standard
Model and to search for new physics. Most previous studies depend on
pre-selected coordinates, which blurs the significance of the results. The
construction of two rotation-invariant observables in vector boson decay into a
fermion pair has been proved to be a big success. In this work, we show that
there are more rotation-invariant observables and provide a general recipe to
find all of them in an arbitrary decay process. Taking spin-1/2 and spin-1
particle decay processes as examples, we calculate the explicit expressions of
all rotation-invariant observables, which can serve as a robust test of the
detector acceptance and help the analysis of experimental data.
