  The way the increment statistics of turbulent velocity fluctuations scale
with the increment size is a centerpiece of turbulence theories. We report data
on decaying turbulence in the Max Planck Variable Density Turbulence Tunnel
(VDTT), which show an approach of the inertial range statistics toward a
nontrivial shape at small scales. By correcting for the contributions of energy
decay to the large-scale statistics with a model, we find the scaling exponent
of the second-order velocity increment statistics to be independent of the
Reynolds number and equal to $0.693\pm0.003$ for $2000\lesssim R_{\lambda}
\lesssim 6000$. This is evidence of a universal inertial range at high Reynolds
numbers.
