Geoscientists and engineers are increasingly using denser arrays for continuous seismic monitoring, and often turning to ambient seismic noise interferometry for low-cost near-surface imaging. While ambient noise interferometry greatly reduces acquisition costs, the computational cost of pair-wise comparisons between all sensors can be prohibitively slow or expensive for applications in engineering and environmental geophysics. Double beamforming of noise correlation functions is a powerful technique to extract body waves from ambient noise, but it is typically performed via pair-wise comparisons between all sensors in two dense array patches (scaling as the product of the number of sensors in one patch with the number of sensors in the other patch). By rearranging the operations involved in the double beamforming transform, we propose a new algorithm that scales as the sum of the number of sensors in two array patches. Compared to traditional double beamforming of noise correlation functions, the new method is more scalable, easily parallelized, and does not require raw data to be exchanged between dense array patches.