The dielectric constant of a monolayer with dielectric anisotropy on a material surface is calculated, assuming that a two-dimensional array is formed and the orientational distribution of rod-like molecules is ruled by Boltzmann statistics. The theoretical local electric field acting on dipoles is taken into consideration in this calculation. It is found that at the molecule density where the maximum tilt angle is theta(A) = theta(k) = root 3-1)/2, i.e. A/A(0) = root 3/2 (A(0) = pi l(2), l is the length of the long axis of rod-like molecule), the dielectric anisotropic monolayer films degenerate to dielectric-isotropic films with an apparent electronic polarizability <(alpha)over bar> = (alpha(parallel to) + (alpha(perpendicular to))/2, regardless of molecular configuration. Under the mean-field approximation the biaxial molecules degenerate to uniaxial ones with an apparent dipole moment mu cos theta(D) and the dependence of dielectric constant on g (see Eq. (9)) is found to be linear.