  We initiate a phenomenological study of `universal relations' in composite
Higgs models, which are dictated by nonlinear shift symmetries acting on the
125 GeV Higgs boson. These are relations among one Higgs couplings with two
electroweak gauge bosons (HVV), two Higgses couplings with two electroweak
gauge bosons (HHVV), one Higgs couplings with three electroweak gauge bosons
(HVVV), as well as triple gauge boson couplings (TGC), which are all controlled
by a single input parameter: the decay constant $f$ of the
pseudo-Nambu-Goldstone Higgs boson. Assuming custodial invariance in strong
sector, the relation is independent of the symmetry breaking pattern in the UV,
for an arbitrary symmetric coset $G/H$. The complete list of corrections to
HVV, HHVV, HVVV and TGC couplings in composite Higgs models is presented to all
orders in $1/f$, and up to four-derivative level, without referring to a
particular $G/H$. We then present several examples of universal relations in
ratios of coefficients which could be extracted experimentally. Measuring the
universal relation requires a precision sensitive to effects of dimension-8
operators in the effective Lagrangian and highlights the importance of
verifying the tensor structure of HHVV interactions in the standard model,
which remains untested to date.
