A purely numerical method of determination of approximate values of true anomalies for two celestial bodies in the proximity of their osculating .quasicomplanar elliptic orbits is given. It consIsts in the solution of only one corresponding quadratic equation. This method is particularly suited and efficient for serial work when determining the least distances of orbits of quasicomplanar asteroids, when these distances are small. This method is illustrated by an already examined pair of asteroids, which has allowed the comparison with previously obtained results and made possible to point out the advantage and the simplicity of this new method, which represents a further step when computing the proximities.