Five galaxy groups with properties similar to those of the Local Group have been surveyed for H i clouds with the Arecibo Telescope . In total 300 pointings have been observed on grids of approximately 2.5 \times 1.5 Mpc centred on the groups . The 4.5 \sigma detection limit on the minimal detectable H i masses is approximately 7 \times 10 ^ { 6 } ~ { } \mbox { $ { M } _ { \odot } $ } ( H _ { 0 } = 65 \mbox { $ km s ^ { -1 } Mpc ^ { -1 } $ } ) . All detections could be attributed to optical galaxies ; no significant detections of H i clouds have been made . This null result leads to the conclusion that the total H i mass of intragroup clouds must be less than 10 per cent of the total H i mass of galaxy groups and less than 0.05 per cent of the dynamical mass . The recent hypothesis that Galactic high velocity clouds are Local Group satellite galaxies is highly inconsistent with these observations .