We study the Bose-Einstein condensation of fermionic pairs in the uniform neutron matter by using the concept of the off-diagonal long-range order of the two-body density matrix of the system. We derive explicit formulas for the condensate density $��_c$ and the condensate fraction $��_c/��$ in terms of the scaled pairing energy gap $��/��_F$, where $��_F$ is the Fermi energy. We calculate the condensate fraction $��_c/��$ as a function of the density $��$ by using previously obtained results for the pairing gap $��$. We find the maximum condensate fraction $(��_c/��)_{max}= 0.42$ at the density $��=5.3\cdot 10^{-4}$ fm$^{-3}$, which corresponds to the Fermi wave number $k_F= 0.25$ fm$^{-1}$.

4 pages, 3 figures, to be published in Phys. Rev. C