  It is shown that there is a second properly normalized KNO scaling function,
$nP_n(n/\bar n)=\varphi(z)$, which has certain advantages in the analysis of
KNO scaling. First, the $nP_n$ are not influenced by the statistical and
systematic uncertainties of $\bar n$ hence $\varphi(z)$ provides more selective
power than the original KNO scaling function $\bar nP_n(n/\bar n)=\psi(z)$.
Second, the new scaling function generates scale parameter $\sigma=1$ since it
depends only on the combination of $z$ and the scale parameter of $\psi(z)$. An
analysis of $\varphi(z)$ is given using $e^+e^-$ annihilation data for charged
particle multiplicity distributions.
