Abstract: In this paper, the properties of system consisting of various nuclear species and free nucleons are described by a nuclear statistical equilibrium system consisting of a typical heavy nucleus, a particles, free neutrons and protons.starting from a semiempirical expression for the mass of the heavy nucleus and the entropy (energy) of their excited states, an equation of state is developed by a restricted minimization of the total free energy of a fixed volume of matter at given temperature and electron fraction.his scheme gave good agreement with the equation of El Eid & Hillebrandt at density 10⁹-10¹²g cm^-3 and with lamb et al (ILPR's equation of state at density 10¹²-10¹⁴g cm^-3,ye=3,σ/k=1.5k.The imput physics such as the rate of electron capture on matter has been treated also more carefully.