Brillouin oscillation appears in picosecond ultrasonics for a transparent specimen because of backward light scattering by moving strain pulse. Its amplitude is comparable with those of other responses, such as pulse-echo signals and through-thickness resonance, obscuring these non-Brillouin-oscillation responses. We here find that Brillouin oscillation can be suppressed in a transparent free-standing film by coating both sides with a metallic thin film of appropriate thickness and that this peculiar behavior is caused by strain pulses generated on both sides with a slight phase difference. This phenomenon allowed us to fabricate a Brillouin-oscillation-free diamond free-standing film, which showed a high capability for sensor applications.