  We present a systematic procedure for determining the Hilbert series that
counts the number of independent operators in the Higgs effective field theory.
After removing the redundancies from equation-of-motion and
integration-by-part, we provide an algorithm of treating the redundancy from
the operators involving in spurion fields parametrizing the custodial symmetry
breaking. Furthermore, we utilize the outer automorphism of the Lorentz and
internal symmetries to separate operators with different CP properties. With
these new implements, the Hilbert series up to chiral dimension 10 are
obtained, and CP-even and CP-odd operators can be further divided. Extensions
to all orders are straightforward.
