An uncommon fine structure in the radio spectrum consisting of bursts in absorption was observed with the Chinese Solar Broadband Radiospectrometer (SBRS) in the frequency range of 2.6 - 3.8 GHz during an X3.4/4B flare on 13 December 2006 in active region NOAA 10930 (S05W33). Usual fine structures in emission such as spikes, zebra stripes, and drifting fibers were observed at the peak of every new flare brightening. Within an hour at the decay phase of the event we observed bursts consisting of spikes in absorption, which pulsated periodically in frequency. Their instantaneous frequency bandwidths were found to be in the 75 MHz range. Moreover, in the strongest Type III-like bursts in absorption, the spikes showed stripes of the zebra-pattern (ZP) that drifted to higher frequencies. All spikes had the duration as short as down to the limit of the instrument resolution of ensuremath≈8 ms. The TRACE 195 ̊A images indicate that the magnetic reconnection at this moment occurred in the western edge of the flare loop arcade. Taking into account the presence of the reverse-drifting bursts in emission, in the course of the restoration of the magnetic structures in the corona, the acceleration of the beams of fast particles must have occurred both upward and downward at different heights. The upward beams will be captured by the magnetic trap, where the loss-cone distribution of fast particles (responsible for the emission of continuum and ZP) were formed. An additional injection of fast particles will fill the loss-cone later, breaking the loss-cone distribution. Therefore, the generation of continuum will be quenched at these moments, which was evidenced by the formation of bursts in absorption.