  We use recent data on the $K^- p \to \pi^0 \pi^0 \Sigma^0$ reaction with the
$\pi^0 \Sigma^0$ mass distribution of forming the $\Lambda(1405)$ with a peak
at 1420 MeV and a relatively narrow width of $\Gamma = 38$ MeV, together with
those of the $\pi^- p \to K^0 \pi \Sigma$ reaction to show that there are two
$\Lambda(1405)$ states instead of one as so far assumed.
