  Cosmic rays interact with the Earth's atmosphere to produce $^{14}$C, which
can be absorbed by trees. Therefore, rapid increases of $^{14}$C in tree rings
can be used to probe previous cosmic-ray events. By this method, three $^{14}$C
rapidly increasing events have been found. Plausible causes of these events
include large solar proton events, supernovae or short gamma-ray bursts.
However, due to the lack of measurements of $^{14}$C by year, the occurrence
frequency of such $^{14}$C rapidly increasing events is poorly known. In
addition, rapid increases may be hidden in the IntCal13 data with five-year
resolution. Here we report the result of $^{14}$C measurements using an ancient
buried tree during the period between BC 3388 and 3358. We find a rapid
increase of about 9\textperthousand~ in the $^{14}$C content from BC 3372 to BC
3371. We suggest that this event could originate from a large solar proton
event.
