  From a systematic analysis of the energy-dependence of four
antibaryon-to-baryon ratios relative to the antikaon-to-kaon ratio, we propose
an alternative approach determining the strange-quark chemical potential
($\mu_{\mathrm{s}}$). It is found that $\mu_{\mathrm{s}}$ generically genuinely
equals one-fifth the baryon chemical potential ($\mu_{\mathrm{b}}$). An
additional quantity depending on $\mu_{\mathrm{b}}$ and the freezeout
temperature ($T$) should be added in order to assure averaged strangeness
conversation. This quantity gives a genuine estimation for the possible
strangeness enhancement with the increase in the collision energy. At the
chemical freezeout conditioned to constant entropy density normalized to
temperature cubed, various particle ratios calculated at $T$ and
$\mu_{\mathrm{b}}$ and the resultant $\mu_{\mathrm{s}}$ excellently agree with
the statistical-thermal calculations.
