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Superluminal tunneling of light through a barrier has attracted broad interest in the last several decades. Despite the observation of such phenomena in various systems, it has been under intensive debate whether the transmitted light truly carry the information of the original pulse. Here we report observation of anomalous time response for terahertz electromagnetic pulses passing through thin metal films, with the pulse shape of the transmitted beam faithfully resembling that of the incident beam. A causal theoretical analysis is developed to explain the experiments, though the theory of Special Relativity may confront a challenge in this exceptional circumstance. These findings may facilitate future applications in high-speed optical communication or signal transmission, and may reshape our fundamental understanding about the tunneling of light., Comment: 16 pages, 9 figures. To be submitted to PHYSICAL REVIEW LETTERS