  We propose a new scenario in which the dominant signal for supersymmetry at
the Tevatron are the events having two or three $\tau$ leptons with high $p_T$
accompanied by large missing transverse energy. This signal is very different
from the multijet or multileptons (involving $e$ and/or $\mu$ only) or the
photonic signals that have been extensively investigated both theoretically and
experimentally. A large region of the GMSB parameter space with the lighter
stau as the NLSP allow this possibility. Such a signal may be present in the
past Tevatron data to be analyzed.
