Abstract: It is difficult to establish statistical detection model in non-Gaussian correlated clutter backgrounds when the clutter has a complicated probability density function (PDF) or even no closed expression. Therefore, a fractional lower order eigenfilter (FLOEF) model under the conditions of α-stable clutter distribution is proposed. The proposed model mainly bases on the fractional lower order statistics and the optimum filtering theory, and the optimum filter is obtained with the rule of maximizing the output fractional lower order signal-to-clutter power ratio. The proposed method can whiten the non-Gaussian correlated clutter by using the clutter fractional lower order covariance matrix, so as to greatly improve the signal-to-clutter ratio and detect the radar target in non-Gaussian correlated clutter effectively. Simulations and real data results show that the detection performance of FLOEF obviously outperforms the traditional eigenfilter (EF) in non-Gaussian correlated clutter environments.