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This work presents exchange potentials for specific orbitals calculated by inverting Hartree?Fock wavefunctions. This was achieved by using a Depurated Inversion Method. The basic idea of the method relies on the substitution of Hartree?Fock orbitals and eigenvalues into the Kohn?Sham equation. Through inversion, the corresponding effective potentials were obtained. Further treatment of the inverted potential should be carried on. The depuration is a careful optimization which eliminates the poles and also ensures the fullfilment of the appropriate boundary conditions. The procedure developed here is not restricted to the ground state or to a nodeless orbital and is applicable to all kinds of atoms. As an example, exchange potentials for noble gases and term-dependent orbitals of the lower configuration of Nitrogen are calculated. The method allows to reproduce the input energies and wavefunctions with a remarkable degree of accuracy.