The independent and cumulative fission product yields (FPYs) and their covariance matrices were newly evaluated for thermal- and fast-neutron induced fission and spontaneous fission. We principally evaluated the independent isobaric charge distributions by taking account of available experimental data, especially putting emphasis on the shell and even-odd staggering in the fission yields by applying a Boltzmann factor including the shell and the pairing correction energies for the mass of fission products. Furthermore, the isomeric ratios of FPY were obtained by a systematic calculation based on the Hauser-Feshbach theory. Normalization of the FPY and associated covariance matrices of independent FPY were determined based on the generalised least-square method to make them consistent with important physical constraints. Especially, the FPYs were normalized to be consistent with the mass chain yield of England and Rider. The cumulative FPYs were calculated by following the relevant β-decay chain by using the decay data from JENDL/DD-2015. Finally, we verified the FPYs evaluated presently by considering experimental decay heats, delayed neutron yields, aggregate antineutrino spectra, and results from post-irradiation examination. All the results have shown that the present set of FPYs were consistent with these data and free from trivial problems present in JENDL/FPY-2011.