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Depolarization was observed in channel waveguides fabricated by ion exchange in glass. This depolarization, as much as 10 percent in distances the order of 5 mm, was apparently due to edge roughness of the channels. A theory is introduced which analyzes this depolarization in terms of coupling between the longitudinal field components in linearly polarized modes of rectangular waveguides. In multimode channel guides it is shown that some depolarization will always be present whenever coupling between modes is large enough to create " " lines. It is also shown that comparable depolarization may occur in single mode channel guides.