A calculation is made to estimate the secondary antiproton ( overlineP) spectrum in the atmosphere by the interaction of cosmic rays. Fermi motion of target nucleons has been included for the first time in the determination of the production of overlinePs. As a result, the production of overlineP is higher than the earlier estimates below a few GeV, which increases with decreasing energy of overlineP, and is about a factor 7 at 100 MeV. The energy spectra of overlineP and overlinen are determined as a function of atmospheric depth by taking into account all energy loss processes. The calculations show that the spectral shape of secondary overlinePs below about 2 GeV evolves rapidly over the entire atmosphere. The derived spectra at small depths are useful to make corrections for overlinePs produced in the overlying atmosphere in balloon borne experiments, which are designed to measure the energy spectrum of primary overlinePs. The secondary overlineP/P ratio varies from about 10 -7 at 50 MeV to 4.5 × 10 -3 at 100 GeV. A method is also suggested to make corrections in experiments, in which the overlineP/P ratio can only be determined. A comparison is made with the earlier estimates and the suggestion is made to test the results of this calculation using ground based experiments.