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This paper presents a new hierarchical scheme for detecting ships from high-resolution synthetic aperture radar (SAR) images. The scheme consists of two stages: detection and discrimination. In the detection stage, the existing internal Hermitian product is extended to obtain a new detector. The new detector makes a combined use of the complex coherence among more than two subapertures and the intensity of each subaperture. When the subaperture number is increased, the target/clutter contrast is shown to be improved. Ship candidates are obtained by applying a threshold. Ship discrimination is performed by using one-class classification. The covariance descriptor, developed by Tuzel in 2006, is introduced to SAR ship discrimination as the feature. The traditional one-class quadratic discriminator is used as the discriminator. After this stage, most false alarms are rejected, and the real ship targets in the candidates are maintained. The effectiveness of the proposed scheme is verified using RADARSAT-2 data. Experimental results show that the proposed scheme can detect most ship targets in the image and few false alarms occur.