In this work, a novel technique for real-time clutter rejection in ultrasound Color Flow Imaging (CFI) is proposed. Suppressing undesired clutter signal is important because clutter prohibits an unambiguous view of the vascular network. Although conventional eigen-based filters are potentially efficient in suppressing clutter signal, their performance is highly dependent on proper selection of a clutter to blood boundary which is done manually. Herein, we resolve this limitation by formulating the clutter suppression problem as a foreground-background separation problem to extract the moving blood component. To that end, we adapt the fast Robust Matrix Completion (fRMC) algorithm, and utilize the in-face extended Frank-Wolfe method to minimize the rank of the matrix of ultrasound frames. Our method automates the clutter suppression process, which is critical for clinical use. We name the method RAPID (Robust mAtrix decomPosition for suppressIng clutter in ultrasounD) since the automation step can substantially streamline clutter suppression. The technique is validated with simulation, flow phantom and two sets of in-vivo data. RAPID code as well as most of the data in this paper can be downloaded from RAPID.sonography.ai.