We have previously designed correlation filters that detect multiple views of an object while remaining specific to the object. We now present a method of modifying the filters to reject clutter, which is defined as additive structured noise. The clutter is rejected by adding to the filters components that are designed to force the contribution of the clutter in the output correlation to be zero. The additional clutter-rejection components are orthogonal to the object harmonics and do not affect the detection process. In the specific example of rotation-invariant detection, the resulting filter has two salient features: it recognizes the object regardless of its rotation or intensity and rejects the clutter regardless of its rotation or intensity.