We present a novel method for determining chromatic dispersion profile from a broadband spectral interferogram obtained by using a white-light interferometry technique. The proposed method is based on direct calculations of a second derivative of the registered spectral intensity at extremal points, which in result gives a spectral phase difference derivative further used for dispersion determining. Although the method is best suited for processing interferograms with modulation around a zero level (zero-mean value interferograms) and slowly changing envelope, the conducted numerical tests show that it is highly tolerable to different types of perturbations of the input interference signal. The proposed method can be applied both to spectral interferograms with monotonically changing phase difference as well as containing stationary phase difference points. We demonstrate the effectiveness and accuracy of the proposed method in measurements of chromatic dispersion of commercially available samples like the BK7 glass plate and the Corning SMF-28 optical fiber.