Spectroscopic data recorded by dispersion spectrophotometers is usually degraded by the response function of the instrument. Double- or triple-cascade spectrophotometers use narrow slits to improve their resolving power, but the total flux of the radiation available decreases accordingly, resulting in a lower signal-to-noise ratio (SNR) and longer exposure time. Nevertheless, the spectral resolution can be improved mathematically by removing the effects of the instrument response function. A constrained high-order cumulant algorithm is proposed to blindly deconvolute the measured spectroscopic data and estimate the response function of the instruments simultaneously. Experiments on artificial and real measured spectroscopic data demonstrate the feasibility of this algorithm.