A variational calculation for the bound states of two electrons moving in the field of an electric dipole and repelling each other through the Coulomb potential has been carried out in order to determine whether bound states with respect to detachment of one electron exist. When the expectation value of the Hamiltonian of the two-electron system is minimized and then set equal to the expectation value of the one-electron system, the resulting equation gives a critical minimum dipole charge required to support bound states for a system of two dipole bound electrons. The behavior of these bound states with respect to dipole length is calculated and discussed.