  An abundance of the strangeness that can be induced in a thermalized
quark-gluon plasma (QGP) is considered as a signal of the QGP phase appearing
in the intermediate state of ultra-relativistic heavy-ion collisions. As a
quantitative characteristic of this signal we take the ratio R_{K^+ K^-} =
N_{K^+}/N_{K^-} of the multiplicities of the production of K^+_- mesons. This
ratio is evaluated for a thermalized QGP phase of QCD and for the quark-gluon
system escaped from the QGP phase. For a thermalized QGP phase the ratio R_{K^+
K^-} has been found as a smooth function of a 3-momentum of the K^+_- mesons
and a temperature ranging the values from the region 160 MeV < T <200 MeV. We
show that at the temperature T= 175 MeV our prediction for the ratio
R_{K^+K^-}(q,T = 175) = 1.80^{+ 0.04}_{-0.18} agrees good with the experimental
data of NA49 and NA44 Collaborations on central ultra-relativistic Pb-Pb
collisions at 158 GeV per nucleon: R^{\exp}_{K^+K^-} = 1.80\pm 0.10. For the
ratio of the K^+ and \pi^+ multiplicities we have obtained the value
R_{K^+\pi^+}(q,T = 175) = 0.134\pm 0.014 agreeing good with the experimental
data of NA35 Collaboration on the nucleus-nucleus collisions at 200 GeV per
nucleon R^{\exp}_{K^+\pi^+} = 0.137\pm 0.008.
