We report here the preliminary results of the search for gravitational wave bursts from the 2003 run of the EXPLORER–NAUTILUS experiment. The total common measuring time was 149 days. The detectors had a typical noise spectral amplitude of about 2 × 10−21 Hz−1/2, a bandwidth of the order of 10 Hz and a very good stability. We derive a new upper limit for the GW burst rate, of the order of 0.02 events/day for hRSS ≥ 2 × 10−19, and discuss the implication of this result with respect to the results obtained with the 2001 run