We study the hardness-intensity correlation ( HIC ) in gamma-ray bursts ( GRBs ) .
In particular , we analyze the decay phase of pulse structures in their light curves .
The study comprises a sample of 82 long pulses selected from 66 long bursts observed by the Burst And Transient Source Experiment ( BATSE ) on the Compton Gamma-Ray Observatory .
We find that at least 57 \% of these pulses have HICs that can be well described by a power law .
A number of the other cases can still be explained with the power law model if various limitations of the observations are taken into account .

The distribution of the power law indices \gamma , obtained by modeling the HIC of pulses from different bursts , is broad with a mean of 1.9 and a standard deviation of 0.7 .
We also compare indices among pulses from the same bursts and find that their distribution is significantly narrower .
The probability p of a random coincidence is shown to be very small ( < 2 \times 10 ^ { -5 } ) .
In most cases , the indices are equal to within the uncertainties .
These results demand a physical model to be able to reproduce multiple pulses with similar characteristics for an individual burst , but with a large diversity for pulses from an ensemble of bursts .
This is particularly relevant when comparing the external versus the internal models .

In our analysis , we also use a new method for studying the hardness-intensity correlation , in which the intensity is represented by the peak value of the EF _ { E } spectrum , where E is the energy and F _ { E } is the energy flux spectrum .
We compare it to the traditional method in which the intensity over a finite energy range is used instead , which may be an incorrect measure of the bolometric intensity .
This new method gives stronger correlations and is useful in the study of various aspects of the HIC .
In particular , it produces a better agreement between indices of different pulses within the same burst .
Also , we find that some pulses exhibit a track jump in their HICs , in which the correlation jumps between two power laws with the same index .
We discuss the possibility that the track jump is caused by strongly overlapping pulses .
Based on our findings , the constancy of the index is proposed to be used as a tool for pulse identification in overlapping pulses and examples of its application are given .