  A viable solution to the origin of close binary systems, unaccounted for in
recent theories, is presented. Fragmentation, occurring at the end of the
secondary collapse phase (during which molecular hydrogen is dissociating), can
form binary systems with separations less than 1 au. Two fragmentation modes
are found to occur after the collapse is halted. The first consists of the
fragmentation of a protostellar disc due to rotational instabilities in a
protostellar core, involving both an $m=1$ and an $m=2$ mode. This
fragmentation mechanism is found to be insensitive to the initial density
distribution: it can occur in both centrally condensed and uniform initial
conditions. The second fragmentation mode involves the formation of a rapidly
rotating core at the end of the collapse phase which is unstable to the
axisymmetric perturbations. This core bounces into a ring which quickly
fragments into several components. The binary systems thus formed contain less
than 1 per cent of a solar mass and therefore will need to accrete most of
their final mass if they are to form a binary star system. Their orbital
properties will thus be determined by the properties of the accreted matter.
