  We consider the scalar sector of the effective non-linear electroweak
Lagrangian with a light "Higgs" particle, up to four derivatives in the chiral
expansion. The complete off-shell renormalization procedure is implemented,
including one loop corrections stemming from the leading two-derivative terms,
for finite Higgs mass. This determines the complete set of independent chiral
invariant scalar counterterms required for consistency; these include bosonic
operators often disregarded. Furthermore, new counterterms involving the Higgs
particle which are apparently chiral non-invariant are identified in the
perturbative analysis. A novel general parametrization of the pseudoescalar
field redefinitions is proposed, which reduces to the various usual ones for
specific values of its parameter; the non-local field redefinitions reabsorbing
all chiral non-invariant counterterms are then explicitly determined. The
physical results translate into renormalization group equations which may be
useful when comparing future Higgs data at different energies.
