  In the present work we theoretically analyze the contribution from a
transverse Fermi-liquid collective mode to the transmission of electromagnetic
waves through a thin film of a clean metal in the presence of a strong external
magnetic field. We show that at the appropriate Fermi surface geometry the
transverse Fermi-liquid wave may appear in conduction electrons liquid at
frequencies $\omega$ significantly smaller than the cyclotron frequency of
charge carriers $\Omega$ provided that the mean collision frequency $\tau^{-1}$
is smaller than $\omega.$ Also, we show that in realistic metals size
oscillations in the transmission coefficient associated with the Firmi-liquid
mode may be observable in experiments. Under certain conditions these
oscillations may predominate over the remaining size effects in the
transmission coefficient.
