  The distribution of the $K^\pm\to\pi^\pm\pi^+\pi^-$ decays in the Dalitz plot
has been measured by the NA48/2 experiment at the CERN SPS with a sample of
$4.71\times 10^8$ fully reconstructed events. With the standard Particle Data
Group parameterization the following values of the slope parameters were
obtained: $g=(-21.134\pm0.017)\%$, $h=(1.848\pm0.040)\%$,
$k=(-0.463\pm0.014)\%$. The quality and statistical accuracy of the data have
allowed an improvement in precision by more than an order of magnitude, and are
such as to warrant a more elaborate theoretical treatment, including pion-pion
rescattering, which is in preparation.
