The characteristics of an electromagnetic surface wave interacting with a semi-infinite single stream of a cold collisionless plasma are investigated by taking the plasma as a moving deformable polarized medium. The surface-wave dispersion equation shows the coupling of four waves, which are, approximately, the fast and slow space-charge waves in the plasma stream and the two waves in the free space whose phases progress in the same and opposite directions to the plasma stream. Compared to the analysis which has regarded the plasma stream as an equivalently stationary anisotropic plasma, the surface waves show drastically different characteristics. It is shown that there are no instabilities of the surface waves for any drift velocity of the plasma.