In this paper optimum detection of the weak signal in the non-Gaussian dependent noise is discussed. Under the assumptions that the noise can be expressed as a first-order AR process n_i=ρn_i-1+y_i and only marginal distribution of noise samples and dependent coefficient ρare given，if ρ is small，the optimum strueture of memory and memoryless detectors can be respectively obtained by maxmizing the first-order and the seeond-order approximations of efficacy to ρ.