We present a new correlation method for deriving the F-corona intensity distribution, which is based on the analysis of the evolution of the total and polarized visible light (VL) images. We studied the one-month variation profiles of the total and polarized brightness acquired with Large Angle Spectrometric COronagraph and found that in some regions they are highly correlated. Assuming that the F-corona does not vary significantly on a timescale of one month, we estimated its intensity in the high-correlation regions and reconstructed the corresponding intensity maps both during the solar-minimum and solar-maximum periods. Systematic uncertainties were estimated by performing dedicated simulations. We compared the resulting F-corona images with those determined using the inversion technique and found that the correlation method provides a smoother intensity distribution. We also obtained that the F-corona images calculated for consecutive months show no significant variation. Finally, we note that this method can be applied to the future high-cadence VL observations carried out with the Metis/Solar Orbiter coronagraph.