  Over the last twenty years, it was assumed that the reaction $\pi^-p\to
a^0_0(980)n\to\pi^0\eta n$ at high energies is dominated by $b_1$ Regge pole
exchange. We show that the new Brookhaven and Serpukhov data on the $t$
distributions for this reaction can be explained within the framework of the
Regge pole model only if the $\rho_2$ Regge pole exchange conspiring with its
daughter plays a crucial role. The tentative estimates of the absolute
$\pi^-p\to a^0_0(980)n\to\pi^0\eta n$ reaction cross section are obtained. The
contributions of the one-pion exchange mechanism and the Regge cuts are also
estimated.
