We report a partly variational calculation of biexcitonic states in a
semiconductor quantum wire subjected to a magnetic field. The longitud
inal component of the biexciton wave function is computed variationall
y, while the transverse component is obtained from exact numerical sol
ution of the Schrodinger equation. We find that an external magnetic f
ield squeezes the biexciton wave function, causing the binding energy
to increase substantially. The increase is more pronounced in wider wi
res where the biexcitonic wave function is ''softer'' and hence more s
queezable, This increase can enhance the already giant third-order non
linear susceptibilities predicted for quantum wires, thus making these
systems attractive for applications in nonlinear optics.