  The ratio R_{\eta}=\Gamma(\eta -> \pi^+\pi^-\gamma)/\Gamma(\eta ->
\pi^+\pi^-\pi^0) has been measured by analyzing 22 million \phi \to \eta \gamma
decays collected by the KLOE experiment at DA\PhiNE, corresponding to an
integrated luminosity of 558 pb^{-1}. The \eta \to \pi^+\pi^-\gamma proceeds
both via the \rho resonant contribution, and possibly a non-resonant direct
term, connected to the box anomaly. Our result, R_{\eta}= 0.1856\pm
0.0005_{stat} \pm 0.0028_{syst}, points out a sizable contribution of the
direct term to the total width. The di-pion invariant mass for the \eta ->
\pi^+\pi^-\gamma decay could be described in a model-independent approach in
terms of a single free parameter, \alpha. The determined value of the parameter
\alpha is \alpha = (1.32 \pm 0.08_{stat} +0.10/-0.09_{syst}\pm 0.02_{theo})
GeV^{-2}
