We present a method to measure the relative spectral response of the Pierre Auger Observatory Fluorescence Detector. The calibration was done at wavelengths of 320, 337, 355, 380 and 405 nm using an end-to-end technique in which the response of all detector components are combined in a single measurement. A xenon flasher and notch-filters were used as the light source for the calibration device. The overall uncertainty is 5%.