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Considering the shortage of comparative studies on pulse temporal characteristics between single-peaked short gamma-ray bursts (sGRBs) and double-peaked sGRBs, we examine the pulse properties of a sample of 100 BATSE sGRBs using the BATSE Time-Tagged Event (TTE) data with a 5-ms resolution. 243 individual pulses of the single-peaked, double-peaked and triple-peaked sGRBs are fitted to get their statistical properties such as the pulse asymmetry, amplitude, peak time, and pulse width, etc. For the double-peaked sGRBs, according to the overlapping ratio between two adjacent peaks, we first define two kinds of double-peaked sGRBs as M-loose and M-tight types and find that most of the first pulses are similar to the single-peaked ones. We study the dependence of the Full Width at Half Maximum (FWHM) on the photon energy among different energy bands. Interestingly, it is found that a power-law relation with an index of -0.4 does exist between the FWHM and the photon energy for the single- and double-peaked sGRBs. More interestingly, we notice that the power-law relation with a positive index also exist for several special short bursts. In view of the three typical timescales of pulses, namely the angular spreading timescale, the dynamic timescale, and the cooling timescale, we propose that the diverse power-law indexes together with the profile evolution of GRB pulse can be used as an effective probe to diagnose the structure and evolution of the relativistically jetted outflows.