In ultrasound (US) imaging, delay and sum (DAS) is the most common beamformer, but it leads to low-quality images. Delay multiply and sum (DMAS) was introduced to address this problem. However, the reconstructed images using DMAS still suffer from the level of side lobes and low noise suppression. Here, a novel beamforming algorithm is introduced based on expansion of the DMAS formula. We found that there is a DAS algebra inside the expansion, and we proposed use of the DMAS instead of the DAS algebra. The introduced method, namely double-stage DMAS (DS-DMAS), is evaluated numerically and experimentally. The quantitative results indicate that DS-DMAS results in an approximately 25% lower level of side lobes compared with DMAS. Moreover, the introduced method leads to 23%, 22% and 43% improvement in signal-to-noise ratio, full width at half-maximum and contrast ratio, respectively, compared with the DMAS beamformer. © 2018