  The cosmological origin of $\gamma$-ray bursts (GRBs) is now commonly
accepted and, according to several models for the central engine, GRB sources
should also emit at the same time gravitational waves bursts (GWBs). We have
performed two correlation searches between the data of the resonant
gravitational wave detector AURIGA and GRB arrival times collected in the BATSE
4B catalog. No correlation was found and an upper limit \bbox{$h_{\text{RMS}}
\leq 1.5 \times 10^{-18}$} on the averaged amplitude of gravitational waves
associated with $\gamma$-ray bursts has been set for the first time.
