A high-order statistical-based, blind deconvolution algorithm is proposed for x-ray powder diffraction profiles. Maximizing the kurtosis amplitude of the deconvolved data ensures that only the data with maximized kurtosis amplitude is extracted. The ill-posed nature of deconvolution is, thus, bypassed. Using simulation and experiments, this method is seen to be very robust with respect to noise. The profile resolution is enhanced considerably, and the deconvolved profile fits the pseudo-Voigt profile nicely. However, noise is enhanced in the deconvolved data, so the algorithm may be invalid for experimental data with low signal-to-noise.