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For detecting moving targets in high-resolution sea clutter, an adaptive normalized matched filter (ANMF) detector is restricted in performance, because the nonstationarity of the clutter restricts spatial samples available for clutter covariance matrix estimation and integration duration. To overcome this limitation, this paper proposes a subband ANMF detector. It consists of a prepositive, discrete Fourier transform, modulated filter bank followed by a set of ANMF detectors in individual subbands. The prepositive filter bank is used to decompose high-rate received signals into low-rate subband signals. The subband decomposition realizes clutter suppression outside each subband and improves the short-time stationarity of sea clutter. Improved short-time stationarity and the low rate of the subband signals allow the subband ANMF detector to have longer integration duration than allowed by the traditional ANMF detector. The ANMF detector in each subband performs clutter suppression inside the subband and matched reception of target returns. The experimental results using real sea clutter data show that the subband ANMF detector attains much better detection performance than the traditional ANMF detector does.