Remarks on Koba-Nielsen-Olesen Scaling

It is shown that there is a second properly normalized KNO scaling function, $n{P}_n(n\mathrm{/}\bar{n})=\phi (z)$, which has certain advantages in the analysis of KNO scaling. First, the $n{P}_n$ are not influenced by the statistical and systematic uncertainties of $\bar{n}$ hence $\phi (z)$ provides more selective power than the original KNO scaling function $\bar{n}{P}_n(n\mathrm{/}\bar{n})=\psi (z)$. 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 $\phi (z)$ is given using $e^{+}{e}^{-}$ annihilation data for charged particle multiplicity distributions.