We propose a deconvolution procedure used for deriving a true fluorescence decay waveform, which is applicable to a band-limited measurement system that has a time delay. In general, the fluorescence decay response has a time delay over the excitation light pulse mainly due to the wavelength dependence of the time delay of the response of a photomultiplier tube (PMT). Furthermore, the frequency band is limited instrumentally or often should be cut off purposely at a relatively low frequency to eliminate high frequency noise. In order to extrapolate such a band-limited response function and to perform a deconvolution procedure in a frequency domain, finally, we introduce a delay time parameter in the conventional Gerchberg-Papoulis (GP) algorithm. We also demonstrate that the Hilbert-transform (HT)-based extrapolation method that we have proposed quite recently is equivalent to the GP algorithm. Simulation and experimental results show that the new method is effective.