Abstract: This paper addresses the problem of MIMO radar signal separation with traditional matched filtering (MF) in dependent non-Gaussian clutter, and a fractional lower order linear constrained minimum power beamforming is proposed. In the proposed method, the dependent clutter and the undesired transmitting signals are regarded as interference. By using the fractional lower order statistics of the received signals based on the rule of linear constrained minimum power (LCMP), the FLO-LCMP model is derived. Finally, simulations are given for the MIMO radar signal separation in SG-Alpha stable distribution clutter. The results show that the proposed method is efficient for MIMO radar signal separation in dependent non-Gaussian clutter.