  We evaluate a Laurent expansion in dimensional regularization parameter
$\epsilon=(4-d)/2$ of all the master integrals for four-loop massless
propagators up to transcendentality weight twelve, using a recently developed
method of one of the present coauthors (R.L.) and extending thereby results by
Baikov and Chetyrkin obtained at transcendentality weight seven. We observe
only multiple zeta values in our results. Therefore, we conclude that all the
four-loop massless propagator integrals, with any integer powers of numerators
and propagators, have only multiple zeta values in their epsilon expansions up
to transcendentality weight twelve.
