Continuous flow electrophoresis is a method to separate ions contained in a sample continuously injected into a laminar flow of electrolyte as a cylindrical stream. Usually, the sample is more conductive than the electrolyte, and the charges created at the sample-electrolyte interface lead to electrohydrodynamic distortions which reduce the separation power of this technique. We demonstrate theoretically that the rate of electrohydrodynamic distortion of a cylindrical sample stream can be reduced to zero, by superimposing to the AC field responsible for the separation of a DC field transverse to it and to the flow direction, with an appropriate frequency, and an effective strength equal to that of the DC field. Using a continuous flow electrophoresis chamber, in which such a field is produced using capacitive electrodes, the major predictions of the theory are confirmed. In particular, it is shown that a sample stream more conductive than the carrying electrolyte, which was seriously deformed in the absence of a transverse AC field, recovers its cylindrical shape in presence of the field. The implications of this discovery for the separating power of continuous-flow electrophoresis are discussed.