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The stability of a thin conductive liquid film flowing along a solid wall is an important problem that occurs in many proposed fusion device designs. In this paper we investigate the linear stability of an electrically conductive liquid film of finite thickness in the presence of a strong magnetic field. Inviscid flows of finite and infinite electric conductivity are considered. The magnetic field is found to decrease the unstable growth rate for both finite and infinite conductivity fluids but only narrows the unstable modes for infinite conductivity fluids. Our theory serves as an extension to the classical theory by Chandrasekhar (1961) [1] by considering the finite-thickness and finite-conductivity effects. Keywords: Rayleigh–Taylor instability, PFC, MHD