  We present results of the one-body density matrix (OBDM) and the condensate
fraction n_0 of liquid 4He calculated at zero temperature by means of the Path
Integral Ground State Monte Carlo method. This technique allows to generate a
highly accurate approximation for the ground state wave function Psi_0 in a
totally model-independent way, that depends only on the Hamiltonian of the
system and on the symmetry properties of Psi_0. With this unbiased estimation
of the OBDM, we obtain precise results for the condensate fraction n_0 and the
kinetic energy K of the system. The dependence of n_0 with the pressure shows
an excellent agreement of our results with recent experimental measurements.
Above the melting pressure, overpressurized liquid 4He shows a small condensate
fraction that has dropped to 0.8% at the highest pressure of p = 87 bar.
