Background: Nuclear waste management is considered amongst the major challenges in the field of nuclear energy. A possible means of addressing this issue is waste transmutation in advanced nuclear systems, whose operation requires a fast neutron spectrum. In this regard, the accurate knowledge of neutron-induced reaction cross sections of several (minor) actinide isotopes is essential for design optimization and improvement of safety margins of such systems. One such case is Pu240, due to its accumulation in spent nuclear fuel of thermal reactors and its usage in fast reactor fuel. The measurement of the Pu240(n,f) cross section was previously attempted at the CERN n_TOF facility EAR1 measuring station using the time-of-flight technique. Due to the low amount of available material and the given flux at EAR1, the measurement had to last several months to achieve a sufficient statistical accuracy. This long duration led to detector deterioration due to the prolonged exposure to the high α activity of the fission foils, therefore the measurement could not be successfully completed. Purpose: It is aimed to determine whether it is feasible to study neutron-induced fission at n_TOF/EAR2 and provide data on the Pu240(n,f) reaction in energy regions requested for applications. Methods: The study of the Pu240(n,f) reaction was made at a new experimental area (EAR2) with a shorter flight path which delivered on average 30 times higher flux at fast neutron energies. This enabled the measurement to be performed much faster, thus limiting the exposure of the detectors to the intrinsic activity of the fission foils. The experimental setup was based on microbulk Micromegas detectors and the time-of-flight data were analyzed with an optimized pulse-shape analysis algorithm. Special attention was dedicated to the estimation of the non-negligible counting loss corrections with the development of a new methodology, and other corrections were estimated via Monte Carlo simulations of the experimental setup. Results: This new measurement of the Pu240(n,f) cross section yielded data from 9meV up to 6MeV incident neutron energy and fission resonance kernels were extracted up to 10keV. Conclusions: Neutron-induced fission of high activity samples can be successfully studied at the n_TOF/EAR2 facility at CERN covering a wide range of neutron energies, from thermal to a few MeV.