  A correlation between the intrinsic energy and the burst duration of
non-repeating fast radio bursts (FRBs) has been reported. If it exists, the
correlation can be used to estimate intrinsic energy from the duration, and
thus can provide us with a new distance measure for cosmology. However, the
correlation suffered from small number statistics (68 FRBs) and was not free
from contamination by latent repeating populations, which might not have such a
correlation. How to separate/exclude the repeating bursts from the mixture of
all different types of FRBs is essential to see this property. Using a much
larger sample from the new FRB catalogue (containing 536 FRBs) recently
released by the CHIME/FRB project, combined with a new classification method
developed based on unsupervised machine learning, we carried out further
scrutiny of the relation. We found that there is a weak correlation between the
intrinsic energy and duration for non-repeating FRBs at z < 0.3 with Kendall's
tau correlation coefficient of 0.239 and significance of 0.001 (statistically
significant), whose slope looks similar to that of gamma-ray bursts. This
correlation becomes weaker and insignificant at higher redshifts (z > 0.3),
possibly due to the lack of the faint FRBs at high-z and/or the redshift
evolution of the correlation. The scattering time in the CHIME/FRB catalogue
shows an intriguing trend: it varies along the line obtained from linear fit on
the energy versus duration plane between these two parameters. A possible
cosmological application of the relation must wait for faint FRBs at high-z.
