A second order current and nonconservation of C-parity

The widths of $\tau \to \pi \eta \nu$ and $\eta \to \pi e^+e^-$ decays, in which a second order $\pi \eta$-current participates, are calculated. It is proposed that the charged and neutral $\pi \eta$-currents are components of a single isovector. The upward experimental limitation on the width of the electromagnetic decay $\Gamma (\eta \to \pi e^+e^-)/\Gamma_{tot}<4,5\cdot 10^{-5}$ which disrupts the C-parity makes it possible to acquire an estimate of $\Gamma (\tau \to \pi \eta \nu)/\Gamma_{tot}<5,3\cdot10^{-5}$ for the decay of a $\tau$-lepton.