The crystallographic anisotropy in electromagnetic terahertz radiation from multiferroic BiFeO3 (100), (110), and (111) films suggests the ultrafast depolarization of ferroelectric order as a new mechanism of terahertz emission. This implies that the spontaneous polarization in ferroelectric materials can be manipulated in time scale of picoseconds, thus paving the way to ultrafast data-storage devices based on nonvolatile ferroelectric memories.