  We revisit the isospin-breaking and electromagnetic corrections to the decay
$\tau^-\to\pi^-\pi^0\nu_\tau$, which allow its use as input in the two-pion
contribution to the (leading order) hadronic vacuum polarization part of the
muon anomalous magnetic moment. We extend a previous resonance chiral
Lagrangian analysis, which included those operators saturating the
next-to-leading order chiral low energy constants, by including the
contributions of the next subleading terms. As a result, we improve agreement
between the two-pion tau decay and $e^+e^-$ data and reduce the discrepancy
between experiment and the SM prediction of $a_\mu$ (using $\tau$ input).
