  For the first time, we list the complete and independent set of operators at
the next-to-next-to-leading order (NNLO) in the Higgs effective field theory
(HEFT), also named as the electroweak chiral Lagrangian with the light Higgs
boson. The Young tensor technique utilized in this work guarantees the
completeness and independence of the on-shell amplitude basis while the Adler
zero condition imposes non-linear symmetry on the Nambu-Goldstone bosons that
play the central role in the chiral Lagrangian. The spurion fields are
incorporated into the gauge structure of operators following the
Littlewood-Richardson rule to accommodate custodial symmetry breaking. We
enumerate 11506 (1927574) NNLO operators for one (three) flavor of fermions for
the electroweak chiral Lagrangian with the light Higgs. Below the electroweak
symmetry breaking scale, the dimension-8 standard model effective field theory
(SMEFT) operators could be matched to these HEFT operators at both the NLO and
NNLO orders.
