The influence of a transverse magnetic field on the Kapitza capillary wave traveling down the surface of a falling, conducting liquid film is investigated. It is shown that, for small magnetic Reynolds numbers the range of admissible dimensionless celerity becomes narrower as the Hartmann number increases. When the Hartmann number reaches 4.63 there is but one single admissible wave celerity (1.43). With still stronger field strength, a traveling wave is no longer possible within the linear scheme employed.