A qualitative explanation of a novel melting phenomenon, a layer-by-layer thinning transition, recently discovered in free-standing partially fluorinated liquid-crystal films, is looked for using a phenomenological Landau free energy density formalism. In the thinning process, the number of layers in a particular film-thickness jump depends on the initial number of layers; the temperature at which a jump, occurs also depends on the initial thickness and increases with decreasing number of initial layers. The results of the calculation are in qualitative agreement with the experimental studies of the layer-thinning transitions above the bulk Sm-A-isotropic transition.