  A dilute Bose system with Bose-Einstein condensate is considered. It is shown
that the Hartree-Fock-Bogolubov approximation can be made both conserving as
well as gapless. This is achieved by taking into account all physical
normalization conditions, that is, the normalization condition for the
condensed particles and that for the total number of particles. Two Lagrange
multipliers, introduced for preserving these normalization conditions, make the
consideration completely self-consistent.
