  Observables are believed that they must be Hermitian in quantum theory. Based
on the obviously physical fact that only eigenstates of observable and its
corresponding probabilities, i.e., spectrum distribution of observable are
actually observed, we argue that observables need not necessarily to be
Hermitian. More generally, observables should be reformulated as normal
operators including Hermitian operators as a subclass. This reformulation is
consistent with the quantum theory currently used and does not change any
physical results. The Clauser-Horne-Shimony-Holt (CHSH) inequality is taken as
an example to show that our opinion does not conflict with conventional quantum
theory and gives the same physical results. Reformulation of observables as
normal operators not only coincides with the physical facts but also will
deepen our understanding of measurement in quantum theory.
