The network of resonant bar detectors of gravitational waves resumed coordinated observations within the International Gravitational Event Collaboration (IGEC-2). Four detectors are taking part in this Collaboration: ALLEGRO, AURIGA, EXPLORER and NAUTILUS. We present here the results of the search for gravitational wave bursts over 6 months during 2005, when IGEC-2 was the only gravitational wave observatory in operation. The implemented network data analysis is based on a time coincidence search among AURIGA, EXPLORER and NAUTILUS; ALLEGRO data was reserved for follow-up studies. The network amplitude sensitivity to bursts improved by a factor ≈3 over the 1997-2000 IGEC observations; the wider sensitive band also allowed the analysis to be tuned over a larger class of waveforms. Given the higher single-detector duty factors, the analysis was based on threefold coincidence, to ensure the identification of any single candidate of gravitational waves with high statistical confidence. The false detection rate was as low as 1 per century. No candidates were found.