Power Doppler ultrasound is in widespread clinical use for non-invasive vascular imaging but the most common current method - Delay and Sum (DAS) beamforming - suffers from limited resolution and high side-lobes. Here we propose the Sub-Aperture Angular Multiply and Sum (SAMAS) algorithm; it combines the advantages of two recent non-linear beamformers, Frame Multiply and Sum (FMAS) which uses signal temporal coherence and the acoustic sub-aperture (ASAP) algorithm, which uses signal spatial coherence, respectively. Following in vitro experiments to optimise the algorithm, particularly the use of phase information and sub-aperture pairing, it was evaluated in vivo, first in a rabbit kidney and then in human lymph node, using ultrafast ultrasound images obtained with intravenous contrast agents. The SAMAS algorithm improved the CNR and SNR across all tests, on average raising the CNR by 11 dB and the SNR by 18 dB over DAS in vivo. This work demonstrates a promising vascular imaging method that could have widespread clinical utility.