  We propose a non-Gaussianity test for gravitational wave backgrounds by
combining data streams of multiple detectors. This simple method allows us to
check whether a detected background is "smooth" enough to be consistent with an
inflation-type background, or is contaminated by individually undetectable weak
burst signals. The proposed test would be quite useful for the Big Bang
Observer or DECIGO whose primary target is a background from inflation at
0.1-1Hz where gravitational wave bursts from supernovae of population III stars
might become a troublesome foreground.
