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The curvature effect is explored in the case of extremely short intrinsicemission. Assuming a $\delta$ function emission we get formulas that get rid ofthe impacts from the intrinsic emission duration, which are applicable to anyforms of continuum. The formulas predict that the same form of spectrum couldbe observed at different times, with the peak energy of the spectrum shiftingfrom 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 thetemporal power law index and the spectral power law index will be related by$\alpha =2+\beta $. The analysis shows that there do exist a temporal steepdecay phase and a spectral softening which occur simultaneously, and both arecaused by the shifting of the Band function spectrum. According to theanalysis, we predict that the softening due to the curvature effect will appearat different frequencies; it occurs earlier for higher frequencies and laterfor lower frequencies; the maximum spectral index time follows the$t_{b,max}\propto \nu^{-1}$ law. We also find: the softening duration would belinearly correlated with the maximum spectral index time; the observed$\beta_{min}$ and $\beta_{max}$ are determined by the low and high energyindexes of the observed Band function spectrum. We propose to check thecurvature effect with the $\log f_{\nu}(t)t^{3}$ vs. $log t$ curve which wouldbe in agreement with the $\log \nu f_{\nu}$ vs. $log \nu$ curve. Applying thisto GRB 060614 shows that the peak energy of its observed spectrum is expectedto pass through the observation band at $\sim $175 s.

The softening phenomenon due to the curvature effect: in the case of extremely short intrinsic emission