  We have studied the production and decay of the $f_1(1285)$ into $\pi
a_0(980)$ and $K^* \bar K$ as a function of the mass of the resonance and find
a shoulder around 1400 MeV, tied to a triangle singularity, for the $\pi
a_0(980)$ mode, and a peak around 1420 MeV with about 60 MeV width for the $K^*
\bar K$ mode. Both these features agree with the experimental information on
which the $f_1(1420)$ resonance is based. In addition, we find that if the
$f_1(1420)$ is a genuine resonance, coupling mostly to $K^* \bar K$ as seen
experimentally, one finds unavoidably about a 20\% fraction for $\pi a_0(980)$
decay of this resonance, in drastic contradiction with all experiments.
Altogether, we conclude that the $f_1(1420)$ is not a genuine resonance, but
the manifestation of the $\pi a_0(980)$ and $K^* \bar K$ decay modes of the
$f_1(1285)$ at higher energies than the nominal one.
