  Clauser-Horne-Shimony-Holt inequality can give values between the classical
bound, 2, and Tsirelson's bound, 2 \sqrt 2. However, for a given set of local
observables, there are values in this range which no quantum state can attain.
We provide the analytical expression for the corresponding bound for a
parametrization of the local observables introduced by Filipp and Svozil, and
describe how to experimentally trace it using a source of singlet states. Such
an experiment will be useful to identify the origin of the experimental errors
in Bell's inequality-type experiments and could be modified to detect
hypothetical correlations beyond those predicted by quantum mechanics.
