Equation of State for the Quark Gluon Plasma with the Negative Bag Constant arXiv:1001.3139v2 [hep-ph] 19 Feb 2010 Viktor V. Begun, 1, 2 Mark I. Gorenstein, 1, 2 and Oleg A. Mogilevsky 1 $^{1}$Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine $^{2}$Frankfurt Institute for Advanced Studies, Frankfurt, Germany We propose a new analytical form of the quark-gluon plasma equation of state (EoS). This new EoS satisfies all qualitative features observed in the lattice QCD calculations and gives a good quantitative description of the lattice results in the SU(3) gluodynamics. The energy density for the suggested EoS looks similar to that in the bag model, but requires a negative value of the bag constant. PACS numbers: 12.39.Ba, 12.40.Ee, 12.38.Mh. Keywords: Bag model, quark gluon plasma, equation of state 1 Abstract