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In this paper a new algorithm for detection of a single complex sinusoid ("cisoid") in white noise is presented. The frequency, phase and amplitude of the cisoid are assumed to be unknown. It is shown that a byproduct of a new class of fast single-cisoid frequency estimation algorithms can replace an MLE-derived quantity in the standard generalized likelihood ratio test (GLRT). This leads to much lower computational cost than the standard GLRT. The price paid is a small increase in the SNR required for effective operation.