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The Radon-ambiguity transform (RAT), although efficient for detecting the linear frequency modulated signals (LFMs), is troubled by the energy accumulation of noise in low signal-to-noise ratio (SNR). A second-order difference (SOD) method is proposed to treat with this problem. In the SOD method, the optimal search step and difference step are derived from the LFM rate resolution formula. The sharpness of the peaks of RAT is measured by curvature, and the sharpness, but not the magnitude of the peaks, is used to detect the LFMs. The SOD method removes the noise energy accumulation and reserves the drastically changing components integrally; thus, it improves the detection probability of LFMs in low SNR. The expected performance of the new method is verified by 100 Monte Carlo simulations.