  A new method is proposed for the calculation of full density matrix and
thermodynamic functions of a many-boson system. Explicit expressions are
obtained in the pair correlations approximation for an arbitrary temperature.
The theory is self-consistent in the sence that the calculated properties at
low temperatures coincide with that of Bogoliubov theory and in the
high-temperature limit lead to the results for classical non-ideal gas in the
random phase approximation. The phase transition is also revealed as a
concequence of Bose-Einstein condensation deformed by interatomic interactions.
All the final formulae are written solely via the liquid structure factor taken
as a source information instead of the interatomic potential and, therefore,
interconnect only observable quantities. This gives also a possibility to study
such a strongly non-ideal system as liquid He-4.
