A viable solution to the origin of close binary systems, unaccounted f
or in recent theories, is presented. Fragmentation, occurring at the e
nd of the secondary collapse phase (during which molecular hydrogen is
dissociating), can form binary systems with separations less than 1 a
u. Two fragmentation modes are found to occur after the collapse is ha
lted. The first consists of the fragmentation of a protostellar disc d
ue to rotational instabilities in a protostellar core, involving both
an m = 1 and an m = 2 mode. This fragmentation mechanism is found to b
e insensitive to the initial density distribution: it can occur in bot
h centrally condensed and uniform initial conditions. The second fragm
entation mode involves the formation of a rapidly rotating core at the
end of the collapse phase which is unstable to the axisymmetric pertu
rbations. This core bounces into a ring which quickly fragments into s
everal components. The binary systems thus formed contain less than 1
per cent of a solar mass and therefore will need to accrete most of th
eir 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.