  The curvature effect is explored in the case of extremely short intrinsic
emission. Assuming a $\delta$ function emission we get formulas that get rid of
the impacts from the intrinsic emission duration, which are applicable to any
forms of continuum. The formulas predict that the same form of spectrum could
be observed at different times, with the peak energy of the spectrum shifting
from higher energy bands to lower bands following $E_{peak}\propto t^{-1}$.
When the emission is early enough the light curve in the form $f_{\nu
}(t)t^{2}$ will possess exactly the intrinsic spectral form, for which the
temporal power law index and the spectral power law index will be related by
$\alpha =2+\beta $. The analysis shows that there do exist a temporal steep
decay phase and a spectral softening which occur simultaneously, and both are
caused by the shifting of the Band function spectrum. According to the
analysis, we predict that the softening due to the curvature effect will appear
at different frequencies; it occurs earlier for higher frequencies and later
for lower frequencies; the maximum spectral index time follows the
$t_{b,max}\propto \nu^{-1}$ law. We also find: the softening duration would be
linearly correlated with the maximum spectral index time; the observed
$\beta_{min}$ and $\beta_{max}$ are determined by the low and high energy
indexes of the observed Band function spectrum. We propose to check the
curvature effect with the $\log f_{\nu}(t)t^{3}$ vs. $log t$ curve which would
be in agreement with the $\log \nu f_{\nu}$ vs. $log \nu$ curve. Applying this
to GRB 060614 shows that the peak energy of its observed spectrum is expected
to pass through the observation band at $\sim $175 s.
