  We extend a previous bispectrum analysis of the Cosmic Microwave Background
temperature anisotropy, allowing for the presence of correlations between
different angular scales. We find a strong non-Gaussian signal in the
``inter-scale'' components of the bispectrum: their observed values concentrate
close to zero instead of displaying the scatter expected from Gaussian maps.
This signal is present over the range of multipoles $\ell=6 -18$, in contrast
with previous detections. We attempt to attribute this effect to galactic
foreground contamination, pixelization effects, possible anomalies in the
noise, documented systematic errors studied by the COBE team, and the effect of
assumptions used in our Monte Carlo simulations. Within this class of
systematic errors the confidence level for rejecting Gaussianity varies between
97% and 99.8%.
