Maximum average correlation height (MACH) filter is formulated by linearly combining the training data, which is statistically optimum and fairly robust for finding targets in clutter when the Gaussian assumption holds. This research proposes a nonlinear extension to the MACH filter by correntropy function which can induce a new feature space. Thus it is possible to construct linear filter equations in the new space, and the proposed filter has an improved performance due to the nonlinear relation between the feature space and input space. The algorithm is applied to synthetic aperture radar image recognition and exhibits better performance under peak-sidelobe-ratio and receiver-operating-characteristic criteria.