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A general formalism is developed for the construction of separable potentials, either from a given pseudopotential or directly from the solutions of an atomic all-electron calculation. Such potentials are vital for the recently developed Car-Parrinello method. A subset of separable potentials, proposed by Kleinman and Bylander, has been used often with great success. However, for some atoms the previously used potentials do not reproduce the scattering properties over a sufficiently wide energy range. It is shown that the Kleinman-Bylander form represents the first term of a complete series. When additional terms are kept, the method yields highly accurate results.