Following our previous papers [Nucl. Phys. B 656 (2003) 259, Nucl. Phys. B 664 (2003) 477] we complete the construction of the parafermionic theory with the symmetry ZN based on the second solution of Fateev-Zamolodchikov for the corresponding parafermionic chiral algebra. In the present paper we construct the ZN parafermionic theory for N even. Primary operators are classified according to their transformation properties under the dihedral group ( ZN× Z2, where Z2 stands for the ZN charge conjugation), as two singlets, doublet 1,2,…, N/2-1, and a disorder operator. In an assumed Coulomb gas scenario, the corresponding vertex operators are accommodated by the Kac table based on the weight lattice of the Lie algebra DN/2 . The unitary theories are representations of the coset SOn( N)× SO2( N)/ SOn+2 ( N), with n=1,2,…. We suggest that physically they realise the series of multicritical points in statistical systems having a ZN symmetry.