  We carry out a systematical study of the spectral lag properties of 50
single-pulsed Gamma-Ray Bursts (GRBs) detected by Fermi/GBM. By dividing the
light curves into multiple consecutive energy channels we provide a new
measurement of the spectral lag which is independent on energy channel
selections. We perform a detailed statistical study of our new measurements. We
find two similar power-law energy dependencies of both the pulse arrival time
and pulse width. Our new results on the power-law indices would favor the
relativistic geometric effects for the origin of spectral lag. However, a
complete theoretical framework that can fully account for the diverse energy
dependencies of both arrival time and pulse width revealed in this work is
still missing. We also study the spectral evolution behaviors of the GRB
pulses. We find that the GRB pulse with negligible spectral lag would usually
have a shorter pulse duration and would appear to have a "hardness-intensity
tracking" (HIT) behavior and the GRB pulse with a significant spectral lag
would usually have a longer pulse duration and would appear to have a
"hard-to-soft" (HTS) behavior.
