In the months since the publication of the first results, the noise performance of LISA Pathfinder has improved because of reduced Brownian noise due to the continued decrease in pressure around the test masses, from a better correction of noninertial effects, and from a better calibration of the electrostatic force actuation. In addition, the availability of numerous long noise measurement runs, during which no perturbation is purposely applied to the test masses, has allowed the measurement of noise with good statistics down to 20 mu Hz. The Letter presents the measured differential acceleration noise figure, which is at (1.74 +/- 0.01) fm s(-2)/root Hz above 2 mHz and (6 +/- 1) x 10 fm s(-2)/root Hz at 20 mu Hz, and discusses the physical sources for the measured noise. This performance provides an experimental benchmark demonstrating the ability to realize the low-frequency science potential of the LISA mission, recently selected by the European Space Agency.