A new mechanism for the formation of binary systems through the fragme
ntation of a protostellar disc is presented. This process requires a s
trongly rotationally unstable (to both m = 2 and m = 1 modes), central
accreting object surrounded by a rotationally supported disc of gas w
hich is subject to continuing infall. The central instability becomes
off-centre due to the growth of the m = 1 mode. The interaction of the
spiral arms thus driven into the disc, with the continued infall, giv
es rise to the formation of a self-gravitating secondary body in orbit
around the first. For cores that form without discs, the core evolves
as in past studies of rotational instabilities. In addition to the m
= 2 bar mode, an m = 1 mode develops, allowing the protostar to conver
t some of its spin angular momentum into orbital angular momentum. Fur
thermore, the gravitational torques from the bar directly account for
the outward transfer of angular momentum. For cores that form with sur
rounding discs and with continuing infall, the spiral arms from the co
re move through the disc gathering matter together. The combination of
the m = 2 mode and the displacement of the core from the m = 1 mode a
llows the spiral arms to gather sufficient matter together from the di
sc and the continuing infall to become gravitationally unstable. This
matter then collapses to form a secondary. In cases where there is no
continuing infall on to the disc, the spiral arms (from the m = 1 and
m = 2 modes) are not able to gather sufficient material to form a Jean
s unstable condensation.