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Medical ultrasound image quality is often limited by clutter, which is the dominant mechanism of image degradation. A variety of beamforming methods have been extensively studied to reduce clutter and, thus, enhance ultrasound image quality. This article introduces a new beamforming approach, called covariance matrix-based statistical beamforming (CMSB), to improve the image contrast and preserve the background speckle pattern while simultaneously achieving a high-resolution performance. In CMSB, adaptive selection of subarray length, diagonal reducing, and mean-to-standard-deviation ratio-based subarray averaging are inherently combined to differentiate and reduce off-axis energy effectively. Moreover, rotary averaging prior to diagonal reducing is introduced to preserve speckle statistics. Simulated, experimental, and in vivo datasets were used to evaluate the imaging performance of the proposed method. The quantitative results indicate that, compared with delay-and-sum (DAS) beamforming, CMSB leads to average improvements of 44.5% and 97.3% in lateral resolution and contrast, respectively, in phantom experiments. Our work shows that CMSB is capable of improving image resolution and contrast while maintaining the speckle reliably. Preliminary in vivo study also demonstrates that the CMSB can enhance image contrast and lesion detection.