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The propagation of Lamb waves in silicon plates coated by a very thin two-dimensional phononic film is studied experimentally. The dispersion curves are measured using a laser ultrasonics technique. The data are then compared to the calculated dispersion curves of the uncoated silicon plate. The overall shapes of the lower-order symmetric and antisymmetric Lamb modes are not altered by the thin phononic film, except by the appearing of frequency band gaps at the edges of both the first and the second Brillouin zone. The influence of the filling fraction on the magnitude of the gaps is investigated experimentally.