The site preference of some transition metals during B2-type ordering has been investigated in the ternary Cu0.5 (Zn1-x Mx )0.5 alloys with M = Ti, V, Ag, Au, Cr, Mn, Fe, Co, Ni, Nb, Mo, Hf, Ta, W, Re or Pt (x ≤ 0.01). The statistic-o-thermodynamical theory combined with the electronic theory of alloys has been used to calculate the partial ordering energies, partial short range order parameters and the order-disorder transformation temperatures. The values of partial short range order parameters have been used to determine the site preference of the metal M. The analysis shows that the metals M can be divided into two groups with regard to lattice site occupancy. One group comprising of Cr, Mn, Fe, Co, Ni, Nb, Mo, Hf, Ta, W, Re or Pt was found to prefer Zn sublattice sites, while the second group of Ti, V, Ag or Au atoms prefer Cu sublattice sites. It is found that order-disorder transformation temperature and the site preference of metal M both depend strongly on the partial ordering energies and ternary alloying addition of metal M.