Abstract: The modified median matrix constant false alarm rate (M-CFAR) detection method is proposed based on the maximum eigenvalue, which utilizes the good detection capability of maximum eigenvalue. The median matrix of reference cells is estimated by using different geometric measures on the matrix manifold. Furthermore, the maximum eigenvalue is exploited as the test statistic. We obtain six kinds of modified median matrix detectors, which combine the maximum eigenvalue with different median matrices. The analysis of computational complexity and simulation experiments based on simulated data and real sea clutter data verify the effectiveness of the proposed methods.