[en] The Bijl-Jastrow product of pairs wave function for the ground-state of He⁴ leads inevitably to off-diagonal long-range order. Furthermore, if the pair wave function is constructed to yield the Feynman structure factor S(k) = h/2πk/2Mc, then the occupation number nsub(k) of momentum state k diverges as k^-1 as 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 He⁴ have 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 if there is no condensate in He⁴, then the He-He interactions must lead to a ground-state wave function which cannot be 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 He⁴ may be helpful in this connection. (author)