The production of derived nuclides by the reaction of ²³⁸U with constant nuclear reactor neutron flux for long time is theoretically described. The concentration of each derived nuclide is zero at the beginning, then increases gradually and approaches a saturated value at a certain irradiation time. The whole system (including the parent nuclide ²³⁸U and all its derived nuclides) will be in a state of equilibrium. Upon the reaction with neutron flux, the whole system decreases its concentration at the same rate as ²³⁸U. It constitutes actually a new type of unstable nuclide series which is in work only in the presence of reactor neutron flux. It has been found that the amount of materials consumed by neutron flux reaction is almost converted entirely to fission product. This peculiar property is quite different from the well known four radioactive series, so that it is named the fifth unstable nuclide series.