The Bijl-Jastrow product of pairs wave function for the ground-state of He4leads inevitably to off-diagonal long-range order. Furthermore, if the pair wave function is constructed to yield the Feynman structure factor S(k) = ħk/2Mc, then the occupation number nkof momentum state k diverges as k-1as k → 0. Re-examination by Jackson of the Mook, Scherm and Wilkinson neutron scattering experiment, and more recent neutron inelastic scattering experiments by Cowley and co-workers on liquid He4have raised serious doubts as to the existence of a condensate. Superfluidity without a condensate is therefore briefly discussed and appears possible in principle. It is argued here that,ifthere is no condensate in He4, then the He-He interactionsmustlead to a ground-state wave function whichcannotbe built from a product of pairs, but must include fundamentally three-atom correlations (at least). A study of the pressure dependence of S(k) in He4may be helpful in this connection