We examine the formation of bound coherent clumps within the environment of turbulent molecular clouds, with emphasis on determining the role that turbulent motions play in the star formation process. We use smoothed particle hydrodynamics to simulate small molecular clouds (~30Msolar), in which the gas is initially supported from gravitational collapse by a freely decaying turbulent field, consistent with a Larson relation of σ~L1/2. We show that the turbulent field does not trigger the star formation via local decreases in the Jeans mass, as has been proposed elsewhere in the literature. Instead, the role of the turbulence is simply to provide shocks that dissipate the supporting kinetic energy and generate structure which acts as seeds for the subsequent fragmentation. These structures are initially unbound, but grow through the self-gravity of the larger-scale region. Collapse proceeds once they attain the mean Jeans mass of the cloud. At this point they are in approximate equipartition of kinetic and thermal energies and can thus fragment to form a multiple system during collapse. Multiple systems are thus a natural consequence of star formation in a turbulent environment.