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For the Case of an unmodulated carrier, the detection of an FM click is formulated as the detection of a non-Gaussian random signal embedded in colored Gaussian noise. This correspondence presents an approximation to the optimum detector of FM clicks along with its theoretical performance in terms of probability of false alarm and probability of error. Numerical results are presented in graphical form. The corresponding exact results for detection problems of this type are currently not available. The theoretical results help to explain the known practical result that FM threshold extenders are limited to threshold improvements of only a few dB. For the case of a modulated carrier, some comments concerning detector performance are presented. For comparison purposes, detector performance of a detector based on the heights of local maxima is also presented.