New constraints for non-Newtonian gravity in nanometer range from the improved precision measurement of the Casimir force

We obtain constraints on non-Newtonian gravity following from the improved precision measurement of the Casimir force by means of atomic force microscope. The hypothetical force is calculated in experimental configuration (a sphere above a disk both covered by two metallic layers). The strengthenings of constraints up to 4 times comparing the previous experiment and up to 560 times comparing the Casimir force measurements between dielectrics are obtained in the interaction range 5.9 nm$\leq\lambda\leq 115 $nm. Recent speculations about the presence of some unexplained attractive force in the considered experiment are shown to be unjustified.