  In the standard scenario of isolated low-mass star formation, strongly
magnetized molecular clouds are envisioned to condense gradually into cores,
driven by ambipolar diffusion. Once the cores become magnetically
supercritical, they collapse to form stars. Most previous studies based on this
scenario are limited to axisymmetric calculations leading to single
supercritical core formation. The assumption of axisymmetry has precluded a
detailed investigation of cloud fragmentation, generally thought to be a
necessary step in the formation of binary and multiple stars. In this
contribution, we describe the non-axisymmetric evolution of initially
magnetically subcritical clouds using a newly-developed MHD code. It is shown
that non-axisymmetric perturbations of modest fractional amplitude ($\sim 5%$)
can grow nonlinearly in such clouds during the supercritical phase of cloud
evolution, leading to the production of either a highly elongated bar or a set
of multiple dense cores.
