PACS numbers : 26.60.+c, 97.60.Jd, 76.60.Jx It is explicitly shown that if phase transition occurs at the core of a newborn neutron star with moderately strong magnetic field strength, which populates only the electron's Landau levels, then in the β-equilibrium condition, the quark core is energetically much more unstable than the neutron matter of identical physical condition. *