  We generalize the Elliott-Yafet (EY) theory of spin relaxation in metals with
inversion symmetry for the case of large spin-orbit coupling (SOC). The EY
theory treats the SOC to the lowest order but this approach breaks down for
metals of heavy elements (such as e.g. caesium or gold), where the SOC energy
is comparable to the relevant band-band separation energies. The generalized
theory is presented for a four-band model system without band dispersion, where
analytic formulae are attainable for arbitrary SOC for the relation between the
momentum- and spin-relaxation rates. As an extended description, we also
consider an empirical pseudopotential approximation where SOC is deduced from
the band potential (apart from an empirical scaling constant) and the
spin-relaxation rate can be obtained numerically. Both approaches recover the
usual EY theory for weak SOC and give that the spin-relaxation rate approaches
the momentum-relaxation rate in the limit of strong SOC. We argue that this
limit is realized in gold by analyzing spin relaxation data. A calculation of
the $g$-factor shows that the empirical Elliott-relation, which links the
$g$-factor and spin-relaxation rate, is retained even for strong SOC.
