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 $rho_c$ and the condensate fraction $rho_c/rho$ in terms of the scaled pairing energy gap $Delta/epsilon_F$, where $epsilon_F$ is the Fermi energy. We calculate the condensate fraction $rho_c/rho$ as a function of the density $rho$ by using previously obtained results for the pairing gap $Delta$. We find the maximum condensate fraction $(rho_c/rho)_{max}= 0.42$ at the density $rho=5.3cdot 10^{-4}$ fm$^{-3}$, which corresponds to the Fermi wave number $k_F= 0.25$ fm$^{-1}$.
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