The technology of synthesis of the nonparametric algorithms for processing of correlated random processes is proposed. The use of a Markov model of correlated signals allows to build Markov copula and synthesize the nonparametric rank algorithms on a single N-cube that use nonparametric estimation of a onedimensional cumulative distribution function using a training sample containing interference only. The theory of synthesis of nonparametric rank Markov decision rules is constructed, the problem of synthesis of rank nonparametric algorithm for detection of correlated signal against the background of uncorrelated noise on the output of amplitude demodulator is solved. Properties of this algorithm are investigated.