SECOND-harmonic generation (SHG)-the frequency doubling of light-requires materials with a non-centrosymmetric structure that gives rise to a large second-order nonlinear optical susceptibility, For molecular materials, it is widely assumed that the molecular structure, as well as the packing arrangement, must also be non-centrosymmetric, unless a magnetic dipole(1-3) or an electric quadrupole(4) contributes to the bulk susceptibility. Consequently, most studies have focused on dipolar molecular systems in which the optical nonlinearities arise from intramolecular charge transfer(5-8). But the criteria for SHG may also be satisfied by centrosymmetric molecules if they aggregate in a non-centrosymmetric manner and there is a contribution to the bulk susceptibility from intermolecular charge transfer. Here we report the nonlinear optical properties of a series of centrosymmetric dyes based on a squaraine template, which we ascribe to such an effect. Monolayer films of these molecules deposited by the Langmuir-Blodgett (LB) technique show surprisingly large SHG, which compares favourably with the highest hitherto reported for LB monolayers of noncentrosymmetric molecules.