  We show how it is possible to give a precise and unambiguous implementation
of the Witten--Veneziano formula for the eta' mass on the lattice, which looks
like the formal continuum one, if the expression of the topological charge
density operator, suggested by fermions obeying the Ginsparg--Wilson relation,
is employed. By using recent numerical results from simulations with overlap
fermions in 2 (abelian Schwinger model) and 4 (QCD) dimensions, one obtains
values for the mass of the lightest pseudo-scalar flavour-singlet state that
agree within errors with theoretical expectations and experimental data,
respectively.
