Using 3D hydrodynamical simulations, we study the fragmentation of uni
form, isothermal, elongated molecular clouds, which are slowly rotatin
g around an axis perpendicular to their elongation. We argue that this
process could result in the formation of binary and multiple stars. T
his new method for forming binary stars can explain widely separated b
inaries with large eccentricities and various mass ratios. At relative
ly low Jeans numbers J0 (the ratio of the binding energies to thermal
energies), a simple binary system is formed. For higher J0, multiple f
ragmentation occurs between the binary fragments, forming a multiple s
ystem. This spontaneous additional fragmentation is induced by rotatio
n. The addition of an angular momentum component parallel to the axis
of elongation complicates this scenario. At low J0, a simple binary is
still formed. At higher J0, multiple fragmentation no longer occurs b
etween the binary fragments but instead the binary fragments themselve
s can fragment through an intermediary bar stage, or through an interm
ediary fragment-disk stage.